Refactor API layer into structured domain-specific modules

- Created new api/ directory with domain-specific API modules:
  - api/client.ts: Base API client with error handling
  - api/auth.ts: Authentication endpoints
  - api/exchange.ts: Exchange/price endpoints
  - api/trades.ts: User trade endpoints
  - api/profile.ts: Profile management endpoints
  - api/invites.ts: Invite endpoints
  - api/admin.ts: Admin endpoints
  - api/index.ts: Centralized exports

- Migrated all API calls from ad-hoc api.get/post/put to typed domain APIs
- Updated all imports across codebase
- Fixed test mocks to use new API structure
- Fixed type issues in validation utilities
- Removed old api.ts file

Benefits:
- Type-safe endpoints (no more string typos)
- Centralized API surface (easy to discover endpoints)
- Better organization (domain-specific modules)
- Uses generated OpenAPI types automatically

frontend/app/api/index.ts

@@ -0,0 +1,12 @@
+/**
+ * Centralized API exports.
+ * Import domain-specific APIs from here.
+ */
+
+export { ApiError, client } from "./client";
+export { authApi } from "./auth";
+export { exchangeApi } from "./exchange";
+export { tradesApi } from "./trades";
+export { profileApi } from "./profile";
+export { invitesApi } from "./invites";
+export { adminApi } from "./admin";