chore: dockerize api proxy and add gitignore

Add a Docker-based FastAPI proxy skeleton (charter §4) for parity across
dev / homelab VPS / fly.io, plus root .gitignore for Godot 4.7 and Python.

- api/Dockerfile: python:3.12-slim, non-root, PORT-aware CMD
- api/app/main.py: /health + five role endpoint stubs (§4)
- api/requirements.txt: fastapi/uvicorn/httpx/pydantic, pinned
- docker-compose.yml: local dev with live reload
- api/fly.toml: prod deploy stub with /health check
- api/.env.example: key lives in the proxy, never the client (§4)
- .gitignore: ignores .env, whitelists .env.example

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

api/.dockerignore

@@ -0,0 +1,16 @@
+# Keep the build context small and secrets out of the image.
+.env
+.env.*
+__pycache__/
+*.py[cod]
+.venv/
+venv/
+.pytest_cache/
+.mypy_cache/
+.ruff_cache/
+.coverage
+htmlcov/
+docs/
+README.md
+Dockerfile
+.dockerignore