Can I vibecode TranscriptAPI?

Build me a small YouTube transcript API service, a personal stand-in for TranscriptAPI.
Requirements:
- Python 3.11 stack: FastAPI, uvicorn, and the youtube-transcript-api library; no
  database, one file plus a README is fine.
- GET /transcript?video=<id-or-url>: extract the video id, fetch the caption track,
  return JSON with the full text plus timestamped segments.
- Support lang= with a sensible fallback to the first available track, and report
  which track was actually used in the response.
- Clean JSON errors: 404 when captions are disabled or missing, 502 when YouTube
  blocks the fetch; never a bare 500.
- Read an optional comma-separated PROXIES var from .env and rotate per request;
  with none set, run direct.
- GET /health returning version and uptime.
- A tiny CLI example in the README: curl the endpoint, jq out the text.
- Keep it stateless and private: no accounts, no API keys, no telemetry, no storage.
- README must be honest about the failure mode: at any real volume YouTube
  rate-limits and IP-blocks caption fetches, and this build has no defense.
- Out of scope, deliberately: the rotating proxy pool and anti-blocking
  infrastructure, channel/playlist/search endpoints, bulk throughput, and SLAs.
  That reliability layer is the thing the paid product actually sells.