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>

.claude/settings.local.json

@@ -0,0 +1,18 @@
+{
+  "permissions": {
+    "allow": [
+      "WebFetch(domain:stitch.withgoogle.com)",
+      "Bash(curl -s -L \"https://stitch.withgoogle.com/preview/1188087097403086912?node-id=a711e3bd0ffd4ff5b8e403ecdb54f247\")",
+      "WebSearch",
+      "Bash(flutter analyze *)",
+      "Bash(flutter *)",
+      "PowerShell(Get-Content *)",
+      "Bash(git push *)",
+      "Bash(git pull *)",
+      "Bash(git checkout *)",
+      "Bash(git reset *)",
+      "Bash(git rm *)",
+      "Bash(rtk git *)"
+    ]
+  }
+}