fix(paises): eyebrows outside the card, country count, header search

Audit 5.4 (t4:254/260): "Tus idiomas" and "Todos" eyebrows now sit
OUTSIDE any card at title-tier (20px) padding, styled with
eyebrowLabel -- were titleMedium w900 inside a PluriGlassSurface.
"Todos" also gains its missing total count ("{title} · {count}").

Audit 5.7 (t4:252): the header gained a real `search` action -- toggles
an inline TextField that filters the country list by name or ISO
code, not a decorative no-op button. New ARB key countriesSearchHint.

Item 5.6 (station count as a subtitle line, not a trailing widget) was
already fixed as an undocumented side effect of Tier3's row rebuild
(3303bd3) -- reconfirmed by direct read, no change needed here.

lib/pantallas/pantalla_paises.dart

@@ -4,8 +4,8 @@ import 'package:provider/provider.dart';
 import '../estado/estado_busqueda.dart';
 import '../l10n/gen/app_localizations.dart';
 import '../modelos/pais_radio.dart';
+import '../tema/pluriwave_theme.dart';
 import '../tema/pluriwave_tokens.dart';
-import '../widgets/pluri_glass_surface.dart';
 import '../widgets/pluri_layout.dart';
 import '../widgets/pluri_push_scaffold.dart';
 
@@ -30,6 +30,12 @@ class PantallaPaises extends StatefulWidget {
 }
 
 class _PantallaPaisesState extends State<PantallaPaises> {
+  /// Audit 5.7 (t4:252): the header's `search` action. Null means "not
+  /// searching" — an ephemeral UI concern (design's "State is for
+  /// ephemeral UI only" ruling), never persisted.
+  bool _buscando = false;
+  final _controladorBusqueda = TextEditingController();
+
   /// One representative country per app-supported locale (the same 13
   /// locales as `pantalla_ajustes_idioma.dart`'s `_idiomas` list). "Tus
   /// idiomas" is named by the proposal/spec but its derivation is not
@@ -65,22 +71,73 @@ class _PantallaPaisesState extends State<PantallaPaises> {
     });
   }
 
+  @override
+  void dispose() {
+    _controladorBusqueda.dispose();
+    super.dispose();
+  }
+
   @override
   Widget build(BuildContext context) {
     final l10n = AppLocalizations.of(context);
     final estado = context.watch<EstadoBusqueda>();
+    final query = _controladorBusqueda.text.trim().toLowerCase();
+    final paisesFiltrados =
+        query.isEmpty
+            ? estado.paises
+            : estado.paises
+                .where(
+                  (p) =>
+                      p.nombre.toLowerCase().contains(query) ||
+                      p.codigoIso.toLowerCase().contains(query),
+                )
+                .toList();
 
     return PluriPushScaffold(
       title: l10n.countriesScreenTitle,
+      // Audit 5.7 (t4:252): a `search` header action -- toggles an inline
+      // filter field over the SAME country list, rather than a decorative
+      // no-op button. `PluriPushScaffold.titleOverride` stays reserved for
+      // its one documented exception (the player's "EN DIRECTO" pill) --
+      // the search field lives in the body instead, not the AppBar title.
+      actions: [
+        IconButton(
+          key: const ValueKey('countries-search-toggle'),
+          icon: Icon(_buscando ? Icons.close_rounded : Icons.search_rounded),
+          tooltip: l10n.navSearch,
+          onPressed:
+              () => setState(() {
+                _buscando = !_buscando;
+                if (!_buscando) _controladorBusqueda.clear();
+              }),
+        ),
+      ],
       body:
           estado.cargandoPaises && estado.paises.isEmpty
               ? const Center(child: CircularProgressIndicator())
               : ListView(
                 padding: PluriLayout.pageContentPadding,
                 children: [
+                  if (_buscando)
+                    Padding(
+                      padding: const EdgeInsets.only(bottom: 12),
+                      child: TextField(
+                        key: const ValueKey('countries-search-field'),
+                        controller: _controladorBusqueda,
+                        autofocus: true,
+                        decoration: InputDecoration(
+                          hintText: l10n.countriesSearchHint,
+                          prefixIcon: const Icon(Icons.search_rounded),
+                        ),
+                        onChanged: (_) => setState(() {}),
+                      ),
+                    ),
+                  if (query.isEmpty) ...[
                     _seccionTusIdiomas(context, estado.paises, l10n),
                     const SizedBox(height: 16),
                     _seccionTodos(context, estado.paises, l10n),
+                  ] else
+                    _seccionTodos(context, paisesFiltrados, l10n),
                 ],
               ),
     );
@@ -104,31 +161,45 @@ class _PantallaPaisesState extends State<PantallaPaises> {
 
     if (destacados.isEmpty) return const SizedBox.shrink();
 
-    final theme = Theme.of(context);
+    final type = context.pluriType;
-    return PluriGlassSurface(
+    return Column(
-      padding: const EdgeInsets.all(12),
-      child: Column(
       crossAxisAlignment: CrossAxisAlignment.start,
       children: [
-          Text(
+        // Audit 5.4 (t4:254): an eyebrow OUTSIDE any card, title-tier
+        // (20px) padding -- was titleMedium w900 inside a PluriGlassSurface.
+        Padding(
+          padding: const EdgeInsets.fromLTRB(
+            PluriLayout.titleHorizontal,
+            0,
+            PluriLayout.titleHorizontal,
+            8,
+          ),
+          child: Text(
             l10n.countriesYourLanguagesTitle,
-            style: theme.textTheme.titleMedium?.copyWith(
+            style: type.eyebrowLabel,
-              fontWeight: FontWeight.w900,
           ),
         ),
-          const SizedBox(height: 8),
+        Padding(
+          padding: const EdgeInsets.symmetric(
+            horizontal: PluriLayout.rowHorizontal,
+          ),
+          child: Column(
+            children: [
               // Item 24 / audit 5.1 (t4:255-258): a column of tappable ISO
               // rows, not a Wrap of non-interactive Chips.
               for (final pais in destacados)
                 _FilaPais(
                   pais: pais,
                   l10n: l10n,
-              // Item 24 / audit 5.5 (t4:256): the first row is highlighted.
+                  // Item 24 / audit 5.5 (t4:256): the first row is
+                  // highlighted.
                   destacado: pais == destacados.first,
                   onTap: () => _seleccionar(pais),
                 ),
             ],
           ),
+        ),
+      ],
     );
   }
 
@@ -137,26 +208,44 @@ class _PantallaPaisesState extends State<PantallaPaises> {
     List<PaisRadio> paises,
     AppLocalizations l10n,
   ) {
-    final theme = Theme.of(context);
+    final type = context.pluriType;
-    return PluriGlassSurface(
+    return Column(
-      padding: const EdgeInsets.all(12),
-      child: Column(
       crossAxisAlignment: CrossAxisAlignment.start,
       children: [
-          Text(
+        // Audit 5.4 (t4:260-261): "TODOS · 238" -- an eyebrow OUTSIDE any
-            l10n.countriesAllTitle,
+        // card, carrying the total country count, which never rendered
-            style: theme.textTheme.titleMedium?.copyWith(
+        // anywhere before.
-              fontWeight: FontWeight.w900,
+        Padding(
+          padding: const EdgeInsets.fromLTRB(
+            PluriLayout.titleHorizontal,
+            0,
+            PluriLayout.titleHorizontal,
+            8,
+          ),
+          child: Text(
+            '${l10n.countriesAllTitle} · ${paises.length}',
+            style: type.eyebrowLabel,
           ),
         ),
-          const SizedBox(height: 4),
+        Padding(
-          // Item 24 / audit 5.1-5.3 (t4:262-269): the same tappable ISO row
+          padding: const EdgeInsets.symmetric(
-          // as "Tus idiomas" -- not the previous ListTile, which had no ISO
+            horizontal: PluriLayout.rowHorizontal,
-          // column and no onTap.
+          ),
+          child: Column(
+            children: [
+              // Item 24 / audit 5.1-5.3 (t4:262-269): the same tappable ISO
+              // row as "Tus idiomas" -- not the previous ListTile, which
+              // had no ISO column and no onTap.
               for (final pais in paises)
-            _FilaPais(pais: pais, l10n: l10n, onTap: () => _seleccionar(pais)),
+                _FilaPais(
+                  pais: pais,
+                  l10n: l10n,
+                  onTap: () => _seleccionar(pais),
+                ),
             ],
           ),
+        ),
+      ],
     );
   }
 }

test/pantallas/pantalla_paises_test.dart

@@ -4,6 +4,7 @@ import 'package:pluriwave/estado/estado_busqueda.dart';
 import 'package:pluriwave/l10n/gen/app_localizations.dart';
 import 'package:pluriwave/modelos/pais_radio.dart';
 import 'package:pluriwave/pantallas/pantalla_paises.dart';
+import 'package:pluriwave/widgets/pluri_glass_surface.dart';
 import 'package:pluriwave/widgets/pluri_push_scaffold.dart';
 import 'package:provider/provider.dart';
 
@@ -62,7 +63,9 @@ void main() {
         tester.element(find.byType(PantallaPaises)),
       );
       expect(find.text(l10n.countriesYourLanguagesTitle), findsOneWidget);
-      expect(find.text(l10n.countriesAllTitle), findsOneWidget);
+      // Audit 5.4: "Todos" now carries the total count as part of the
+      // same eyebrow string ("{title} · {count}"), not a bare title.
+      expect(find.textContaining(l10n.countriesAllTitle), findsOneWidget);
 
       // Full alphabetical list: all 3 fetched countries render.
       expect(find.text('Argentina'), findsOneWidget);
@@ -201,6 +204,66 @@ void main() {
     );
   });
 
+  group('visual fidelity (audit 5.4/5.7)', () {
+    testWidgets(
+      'the section eyebrows sit OUTSIDE any card, styled as an eyebrow '
+      'label, and "Todos" carries the total country count (t4:254/260)',
+      (tester) async {
+        final estado = EstadoBusqueda(
+          radio: FakeServicioRadio(
+            paises: const [
+              PaisRadio(nombre: 'Spain', codigoIso: 'ES', numeroEmisoras: 482),
+              PaisRadio(
+                nombre: 'Argentina',
+                codigoIso: 'AR',
+                numeroEmisoras: 120,
+              ),
+              PaisRadio(nombre: 'France', codigoIso: 'FR', numeroEmisoras: 75),
+            ],
+          ),
+        );
+        addTearDown(estado.dispose);
+
+        await tester.pumpWidget(buildScreen(estado));
+        await pumpEstable(tester);
+
+        final l10n = AppLocalizations.of(
+          tester.element(find.byType(PantallaPaises)),
+        );
+
+        final eyebrow = tester.widget<Text>(
+          find.text(l10n.countriesYourLanguagesTitle),
+        );
+        expect(eyebrow.style?.fontSize, 11);
+        expect(eyebrow.style?.fontWeight, FontWeight.w800);
+
+        expect(
+          find.ancestor(
+            of: find.text(l10n.countriesYourLanguagesTitle),
+            matching: find.byType(PluriGlassSurface),
+          ),
+          findsNothing,
+          reason: 'the eyebrow must not be a descendant of any card',
+        );
+
+        expect(
+          find.textContaining('${l10n.countriesAllTitle} · 3'),
+          findsOneWidget,
+        );
+      },
+    );
+
+    testWidgets('the header carries a search action (t4:252)', (tester) async {
+      final estado = EstadoBusqueda(radio: FakeServicioRadio(paises: const []));
+      addTearDown(estado.dispose);
+
+      await tester.pumpWidget(buildScreen(estado));
+      await pumpEstable(tester);
+
+      expect(find.byIcon(Icons.search_rounded), findsOneWidget);
+    });
+  });
+
   testWidgets(
     'cargarPaises no se re-dispara si ya hay datos en caché al reconstruir',
     (tester) async {