Add unit and integration test suites

- Shared: link building, feed ordering, input schemas, API client
- API unit: track matching, private-address blocking, token crypto,
  plan expiry, provider response parsing
- API integration against Postgres and Redis: auth, follows and pins,
  now-playing state, webhooks, OAuth return URLs, realtime, rate limits
- Tests use a dedicated *_test database and Redis DB, and refuse to wipe
  anything else; fetch is stubbed so they never hit the network
- Pin Node to 22.13+ (.nvmrc), which Vite's native bindings require

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01MzFywujuH9TiuXbr9vjoX8

apps/api/tsconfig.json

@@ -1,7 +1,14 @@
 {
   "extends": "../../tsconfig.base.json",
   "compilerOptions": {
-    "types": ["node"]
+    "types": [
+      "node"
+    ]
   },
-  "include": ["src", "drizzle.config.ts"]
+  "include": [
+    "src",
+    "test",
+    "drizzle.config.ts",
+    "vitest.config.ts"
+  ]
 }