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/db.ts

@@ -29,6 +29,7 @@ function mockRowFromInsert(sql: string, params: unknown[]): RaceRow {
       bib_pickup: null,
       bib_number: null,
       finish_time: null,
+      finish_place: null,
       notes: null,
       created_at: now,
       updated_at: null,
@@ -51,6 +52,7 @@ function mockRowFromInsert(sql: string, params: unknown[]): RaceRow {
     bib_pickup: row.bib_pickup != null ? String(row.bib_pickup) : null,
     bib_number: row.bib_number != null ? String(row.bib_number) : null,
     finish_time: row.finish_time != null ? String(row.finish_time) : null,
+    finish_place: row.finish_place != null ? String(row.finish_place) : null,
     notes: row.notes != null ? String(row.notes) : null,
     created_at: now,
     updated_at: null,