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/package.json

@@ -7,7 +7,8 @@
     "dev": "ts-node src/index.ts",
     "start": "node dist/index.js",
     "db:migrate": "ts-node src/migrate.ts",
-    "seed": "ts-node src/seed.ts"
+    "seed": "ts-node src/seed.ts",
+    "test": "CALENDAR_RUN_MOCK_DB=1 tsx --test test/app.test.ts"
   },
   "dependencies": {
     "cors": "^2.8.5",
@@ -21,7 +22,10 @@
     "@types/express": "^5.0.0",
     "@types/node": "^22.12.0",
     "@types/pg": "^8.11.10",
+    "@types/supertest": "^6.0.2",
+    "supertest": "^7.0.0",
     "ts-node": "^10.9.2",
+    "tsx": "^4.19.2",
     "typescript": "^5.7.3"
   }
 }