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/Dockerfile

@@ -0,0 +1,26 @@
+# /api — FastAPI proxy (charter §4). Docker-based for parity across
+# dev / homelab VPS / fly.io.
+FROM python:3.12-slim
+
+# Faster, quieter Python in containers.
+ENV PYTHONUNBUFFERED=1 \
+    PYTHONDONTWRITEBYTECODE=1 \
+    PIP_NO_CACHE_DIR=1
+
+WORKDIR /app
+
+# Install deps first so the layer caches when only app code changes.
+COPY requirements.txt .
+RUN pip install --no-cache-dir -r requirements.txt
+
+# App code.
+COPY app ./app
+
+# Run as non-root.
+RUN useradd --create-home --uid 1000 appuser
+USER appuser
+
+EXPOSE 8000
+
+# fly.io / compose set PORT; default to 8000 (charter localhost:8000).
+CMD ["sh", "-c", "uvicorn app.main:app --host 0.0.0.0 --port ${PORT:-8000}"]