feat: align docs with code, finish_place, registered status, UI filters, tests, CI

- Add PLAN.md and sync backend docs, .env.example, API doc (404 details)
- Document mock DB and PORT/API_PORT in docs/backend.md; README monorepo + frontend/.env.example
- Migration 002: finish_place column, status registered; mapper and mock DB updated
- Frontend: registered status, finishPlace, calendar year/month filters, pace sparkline
- Extract createApp for tests; supertest + tsx; GitHub Actions CI

Made-with: Cursor

backend/src/index.ts

@@ -1,16 +1,7 @@
-import express from "express";
-import cors from "cors";
 import { config } from "./config";
-import healthRouter from "./routes/health";
-import racesRouter from "./routes/races";
+import { createApp } from "./app";
 
-const app = express();
-
-app.use(cors({ origin: config.corsOrigin, methods: ["GET", "POST", "PATCH", "DELETE"] }));
-app.use(express.json());
-
-app.use(healthRouter);
-app.use(racesRouter);
+const app = createApp();
 
 app.listen(config.apiPort, () => {
   console.log(`[api] Listening on http://localhost:${config.apiPort}`);