refactor: organize API around operation domains (#24)

* feat: reorganize API around operation domains

Restructure the oRPC contract from 14 resource-oriented routers to 8
domain-oriented routers for a cleaner public API surface.

- Consolidate 7 watch procedures into unified tracking.watch/unwatch
  with scope + ids input (movie, episode, season, series)
- Split dashboard across tracking (stats, history), library
  (continueWatching, upcoming), and discover (recommendations)
- Merge explore + search + discover into single discover router
- Absorb integrations into account.integrations
- Merge system.authConfig into system.publicInfo
- Collapse 6 admin setting endpoints into admin.settings.get/update
- Deduplicate platforms.list + explore.watchProviders into
  discover.platforms
- Add symmetric unwatchMovie/unwatchSeries core functions
- Rename titles.detail→get, titles.recommendations→similar,
  people.detail→get

BREAKING CHANGE: All client API paths have changed. REST paths now
mirror router structure.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

* fix: address review feedback on API reorganization

- Fix updateRating invalidation in native app — was only invalidating
  title queries, now calls invalidateTitleQueries() to also refresh
  tracking.userInfo (drives the rating UI)
- Make unwatchMovie status revert consistent with unwatchSeries — revert
  any non-watchlist status, not just "completed"
- Add sync invariant comment on handleWatch/handleUnwatch loops
- Remove unused queryClient import in native use-title-actions

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

* fix: updateStatus NOT_FOUND error + rate() invalidation in native

- updateStatus now throws NOT_FOUND when quickAddTitle returns null
  (title doesn't exist), instead of silently succeeding
- Add NOT_FOUND error to updateStatus contract definition
- Fix rate() in native title-actions.ts to call invalidateTitleQueries()
  instead of only invalidating orpc.titles.key() — mirrors the fix
  already applied to the hook-based path in d2ddc0f

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

* docs: expand mobile app docs and add Play Store badge

- Add the Google Play badge to the README alongside the App Store badge
- Expand the mobile app docs with the Android/Play Store release details
- Refresh docs site dependencies and related package versions for the updated docs stack

---------

Co-authored-by: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

docs/package.json

@@ -16,10 +16,10 @@
   "dependencies": {
     "@takumi-rs/image-response": "^0.73.1",
     "@vercel/analytics": "^2.0.1",
-    "fumadocs-core": "^16.7.5",
+    "fumadocs-core": "^16.7.6",
     "fumadocs-mdx": "^14.2.11",
-    "fumadocs-openapi": "^10.4.1",
-    "fumadocs-ui": "^16.7.5",
+    "fumadocs-openapi": "^10.5.0",
+    "fumadocs-ui": "^16.7.6",
     "lucide-react": "^0.577.0",
     "next": "16.2.1",
     "react": "19.2.4",