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/test/app.test.ts

@@ -0,0 +1,39 @@
+import assert from "node:assert/strict";
+import { test } from "node:test";
+import request from "supertest";
+import { createApp } from "../src/app";
+
+const app = createApp();
+
+test("GET /health returns ok", async () => {
+  const res = await request(app).get("/health").expect(200);
+  assert.equal(res.body.status, "ok");
+});
+
+test("GET /ready succeeds with mock database", async () => {
+  const res = await request(app).get("/ready").expect(200);
+  assert.equal(res.body.status, "ready");
+  assert.equal(res.body.db, "connected");
+});
+
+test("GET /races rejects invalid year", async () => {
+  const res = await request(app).get("/races?year=bad").expect(400);
+  assert.equal(res.body.error, "validation_error");
+  assert.ok(Array.isArray(res.body.details));
+});
+
+test("GET /races rejects month out of range", async () => {
+  const res = await request(app).get("/races?month=13").expect(400);
+  assert.equal(res.body.error, "validation_error");
+});
+
+test("GET /races accepts year and month", async () => {
+  const res = await request(app).get("/races?year=2026&month=5").expect(200);
+  assert.ok(Array.isArray(res.body));
+});
+
+test("GET /races/:id returns not_found", async () => {
+  const res = await request(app).get("/races/does-not-exist").expect(404);
+  assert.equal(res.body.error, "not_found");
+  assert.ok(Array.isArray(res.body.details));
+});