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/auth.ts

@@ -0,0 +1,41 @@
+import { client } from "./client";
+import { components } from "../generated/api";
+
+type User = components["schemas"]["UserResponse"];
+
+/**
+ * Authentication API endpoints
+ */
+export const authApi = {
+  /**
+   * Get current authenticated user
+   */
+  getMe(): Promise<User> {
+    return client.get<User>("/api/auth/me");
+  },
+
+  /**
+   * Login with email and password
+   */
+  login(email: string, password: string): Promise<User> {
+    return client.post<User>("/api/auth/login", { email, password });
+  },
+
+  /**
+   * Register a new user with invite code
+   */
+  register(email: string, password: string, inviteIdentifier: string): Promise<User> {
+    return client.post<User>("/api/auth/register", {
+      email,
+      password,
+      invite_identifier: inviteIdentifier,
+    });
+  },
+
+  /**
+   * Logout current user
+   */
+  logout(): Promise<void> {
+    return client.post<void>("/api/auth/logout");
+  },
+};