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/app.ts

@@ -0,0 +1,17 @@
+import express from "express";
+import cors from "cors";
+import { config } from "./config";
+import healthRouter from "./routes/health";
+import racesRouter from "./routes/races";
+
+export function createApp(): express.Express {
+  const app = express();
+
+  app.use(cors({ origin: config.corsOrigin, methods: ["GET", "POST", "PATCH", "DELETE"] }));
+  app.use(express.json());
+
+  app.use(healthRouter);
+  app.use(racesRouter);
+
+  return app;
+}