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/page.tsx

@@ -3,7 +3,7 @@
 import { useEffect, useState, useCallback, useMemo } from "react";
 import { useRouter } from "next/navigation";
 import { Permission } from "../auth-context";
-import { api } from "../api";
+import { exchangeApi, tradesApi } from "../api";
 import { extractApiErrorMessage } from "../utils/error-handling";
 import { Header } from "../components/Header";
 import { LoadingState } from "../components/LoadingState";
@@ -166,7 +166,7 @@ export default function ExchangePage() {
 
     const fetchUserTrades = async () => {
       try {
-        const data = await api.get<ExchangeResponse[]>("/api/trades");
+        const data = await tradesApi.getTrades();
         setUserTrades(data);
       } catch (err) {
         console.error("Failed to fetch user trades:", err);
@@ -242,7 +242,7 @@ export default function ExchangePage() {
     setExistingTradeId(null);
 
     try {
-      await api.post<ExchangeResponse>("/api/exchange", {
+      await exchangeApi.createExchange({
         slot_start: selectedSlot.start_time,
         direction,
         bitcoin_transfer_method: bitcoinTransferMethod,