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

.github/workflows/ci.yml

@@ -0,0 +1,36 @@
+name: CI
+
+on:
+  push:
+    branches: [main, master]
+  pull_request:
+    branches: [main, master]
+
+jobs:
+  build-and-test:
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v4
+
+      - uses: actions/setup-node@v4
+        with:
+          node-version: "20"
+          cache: "npm"
+          cache-dependency-path: |
+            backend/package-lock.json
+            frontend/package-lock.json
+
+      - name: Backend — install, build, test
+        working-directory: backend
+        env:
+          CALENDAR_RUN_MOCK_DB: "1"
+        run: |
+          npm ci
+          npm run build
+          npm test
+
+      - name: Frontend — install, build
+        working-directory: frontend
+        run: |
+          npm ci
+          npm run build