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/signup/page.tsx

@@ -3,15 +3,9 @@
 import { useState, useEffect, useCallback, Suspense } from "react";
 import { useRouter, useSearchParams } from "next/navigation";
 import { useAuth } from "../auth-context";
-import { api } from "../api";
+import { invitesApi } from "../api";
 import { authFormStyles as styles } from "../styles/auth-form";
 
-interface InviteCheckResponse {
-  valid: boolean;
-  status?: string;
-  error?: string;
-}
-
 function SignupContent() {
   const searchParams = useSearchParams();
   const initialCode = searchParams.get("code") || "";
@@ -49,9 +43,7 @@ function SignupContent() {
     setInviteError("");
 
     try {
-      const response = await api.get<InviteCheckResponse>(
-        `/api/invites/${encodeURIComponent(code.trim())}/check`
-      );
+      const response = await invitesApi.checkInvite(code.trim());
 
       if (response.valid) {
         setInviteValid(true);