refactor(native): centralize navigation header configuration into dedicated stack components

Replace the `useTabScreenOptions` hook (and its `.android` variant) with a `TabStack` component that encapsulates all tab-level header styling in one place. Introduce `AuthStackHeader` and `DetailStackHeader` components to own header configuration for auth and detail screens respectively, removing scattered `Stack.Screen options` overrides from individual screen files.

- Delete `use-tab-screen-options.tsx` and `use-tab-screen-options.android.tsx`; all four tab layouts now render `<TabStack title="…" />` instead of manually composing `<Stack screenOptions={useTabScreenOptions()}>`.
- Add `AuthStackHeader` and swap every `<Stack.Screen options={{ title: "…" }}>` inside auth screens for it; strip the now-redundant header option overrides from the auth `_layout`.
- Add `DetailStackHeader` and remove the hardcoded `headerTransparent`/`headerTintColor`/`headerBackButtonDisplayMode` options from the title and person detail routes in `_layout.tsx`.
- Replace remaining `Stack.Screen options={{ title }}` patterns in non-tab screens (`change-password`, `+not-found`) with the `Stack.Screen.Title` helper.
- Refactor the search screen to use `Stack.Header`, `Stack.Screen.Title`, and `Stack.SearchBar` instead of an inline `Stack.Screen options` object; add `placement` and `allowToolbarIntegration` for the iOS integrated search bar.
- Add `browseTitleIds` server procedure and extend `explore` / `discover` procedures; add corresponding schema fields in `@sofa/api`.

packages/api/src/schemas.ts

@@ -451,6 +451,10 @@ export const PersonCreditSchema = z
 /** Reusable TMDB browse result (trending / popular / discover items) */
 export const TmdbBrowseItem = z
   .object({
+    id: z
+      .string()
+      .optional()
+      .describe("Internal title ID when the title already exists locally"),
     tmdbId: z.number().describe("TMDB numeric ID"),
     type: mediaType,
     title: z.string().describe("Display title"),
@@ -690,6 +694,10 @@ export const TrendingOutput = z
     items: z.array(TmdbBrowseItem).describe("Trending titles"),
     hero: z
       .object({
+        id: z
+          .string()
+          .optional()
+          .describe("Internal title ID when the title already exists locally"),
         tmdbId: z.number().describe("TMDB numeric ID"),
         type: mediaType,
         title: z.string().describe("Display title"),