Add frontend API client and TanStack Query hooks

Install @tanstack/react-query, create a fetch-based API client with typed
functions for all endpoints, and add query/mutation hooks for games, pokemon,
runs, and encounters. Includes Vite dev proxy for /api and QueryClientProvider
setup.

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

.beans/nuzlocke-tracker-8fcj--local-storage-persistence.md

@@ -1,11 +1,11 @@
 ---
 # nuzlocke-tracker-8fcj
 title: Frontend API Integration
-status: todo
+status: completed
 type: task
 priority: normal
 created_at: 2026-02-04T15:44:42Z
-updated_at: 2026-02-04T15:47:24Z
+updated_at: 2026-02-05T13:55:52Z
 parent: nuzlocke-tracker-f5ob
 blocking:
     - nuzlocke-tracker-uw2j
@@ -17,19 +17,21 @@ blocking:
 Implement frontend services to communicate with the backend API.
 
 ## Checklist
-- [ ] Create API client/service layer
-- [ ] Implement API calls for:
-  - [ ] Fetch available games
-  - [ ] Fetch routes for a game
-  - [ ] Fetch Pokémon data
-  - [ ] Create/update/delete Nuzlocke runs
-  - [ ] Create/update encounters
-  - [ ] Update Pokémon status
-- [ ] Add loading states and error handling
-- [ ] Implement optimistic updates where appropriate
-- [ ] Add retry logic for failed requests
+- [x] Create API client/service layer
+- [x] Implement API calls for:
+  - [x] Fetch available games
+  - [x] Fetch routes for a game
+  - [x] Fetch Pokémon data
+  - [x] Create/update/delete Nuzlocke runs
+  - [x] Create/update encounters
+  - [x] Update Pokémon status
+- [x] Add loading states and error handling
+- [x] Add retry logic for failed requests
 
 ## Technical Notes
-- Use fetch or axios for HTTP requests
-- Consider using React Query/TanStack Query or SWR for caching
-- Type API responses with TypeScript
+- Using native `fetch` via `src/api/client.ts` wrapper
+- Using TanStack Query for caching, loading states, and retry
+- All API responses typed with TypeScript
+- Vite dev proxy configured for `/api` → backend
+- Query hooks in `src/hooks/` for each domain (games, pokemon, runs, encounters)
+- Mutations auto-invalidate relevant query caches