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/exchange/hooks/useExchangePrice.ts

@@ -1,5 +1,5 @@
 import { useState, useEffect, useCallback } from "react";
-import { api } from "../../api";
+import { exchangeApi } from "../../api";
 import { components } from "../../generated/api";
 
 type ExchangePriceResponse = components["schemas"]["ExchangePriceResponse"];
@@ -37,7 +37,7 @@ export function useExchangePrice(options: UseExchangePriceOptions = {}): UseExch
     setError(null);
 
     try {
-      const data = await api.get<ExchangePriceResponse>("/api/exchange/price");
+      const data = await exchangeApi.getPrice();
       setPriceData(data);
       setLastUpdate(new Date());