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/invites.ts

@@ -0,0 +1,24 @@
+import { client } from "./client";
+import { components } from "../generated/api";
+
+type Invite = components["schemas"]["UserInviteResponse"];
+type InviteCheckResponse = components["schemas"]["InviteCheckResponse"];
+
+/**
+ * Invites API endpoints (user-facing)
+ */
+export const invitesApi = {
+  /**
+   * Get all invites for the current user
+   */
+  getInvites(): Promise<Invite[]> {
+    return client.get<Invite[]>("/api/invites");
+  },
+
+  /**
+   * Check if an invite code is valid
+   */
+  checkInvite(code: string): Promise<InviteCheckResponse> {
+    return client.get<InviteCheckResponse>(`/api/invites/${encodeURIComponent(code)}/check`);
+  },
+};