fix(ci): exclude bin/ from root analyzer and clean remaining warnings

The frontend CI job ran `flutter analyze` from the repo root, which also
analyzed the bin/ server package without its dependencies resolved
(shelf_router, sqlite3, bcrypt, test), producing hundreds of
uri_does_not_exist errors. bin/ is a standalone package covered by the
backend job, so it is now excluded from root analysis.

Also:
- Remove all unused fields/variables flagged as analyzer warnings
  (api_client, cache_service, player_screen, subtitle_service,
  live_tv_tab, mobile screens)
- Run `flutter analyze --no-fatal-infos` in CI: pre-existing deprecation
  infos (withOpacity, dart:html) stay non-fatal while errors and warnings
  still fail the build

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

.github/workflows/ci.yml

@@ -15,7 +15,9 @@ jobs:
         with:
           channel: stable
       - run: flutter pub get
-      - run: flutter analyze
+      # Infos (pre-existing withOpacity/dart:html deprecations) are not
+      # fatal; errors and warnings still fail the build.
+      - run: flutter analyze --no-fatal-infos
       - run: flutter test
       - run: flutter build web --release