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>

analysis_options.yaml

@@ -1,5 +1,11 @@
 include: package:flutter_lints/flutter.yaml
 
+analyzer:
+  exclude:
+    # bin/ is a standalone Dart package (server) with its own pubspec and
+    # analysis; it is analyzed by the backend CI job via `dart analyze`.
+    - bin/**
+
 linter:
   rules:
     - prefer_const_constructors