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/trades/[id]/page.tsx

@@ -3,7 +3,7 @@
 import { useEffect, useState, CSSProperties } from "react";
 import { useParams, useRouter } from "next/navigation";
 import { Permission } from "../../auth-context";
-import { api } from "../../api";
+import { tradesApi } from "../../api";
 import { Header } from "../../components/Header";
 import { SatsDisplay } from "../../components/SatsDisplay";
 import { useRequireAuth } from "../../hooks/useRequireAuth";
@@ -42,7 +42,7 @@ export default function TradeDetailPage() {
       try {
         setIsLoadingTrade(true);
         setError(null);
-        const data = await api.get<ExchangeResponse>(`/api/trades/${publicId}`);
+        const data = await tradesApi.getTrade(publicId);
         setTrade(data);
       } catch (err) {
         console.error("Failed to fetch trade:", err);
@@ -221,7 +221,7 @@ export default function TradeDetailPage() {
                     return;
                   }
                   try {
-                    await api.post(`/api/trades/${trade.public_id}/cancel`, {});
+                    await tradesApi.cancelTrade(trade.public_id);
                     router.push("/trades");
                   } catch (err) {
                     setError(err instanceof Error ? err.message : "Failed to cancel trade");