fix: make database storage part of readiness

[Minorli]

Summary

• make /api/ready validate output storage and the SQLite filesystem with durable temporary write probes
• verify the PicGen database with a short-timeout integrity/schema check and return HTTP 503 when dependencies are not ready
• move Docker health checks to /api/ready and release the synchronized 0.1.67 version

Safety

• keep /api/health as process-only liveness
• cache probes and isolate readiness concurrency from the shared AnyIO worker pool
• preserve all existing database contents and migrations; no runtime dependency changes

Verification

• ./scripts/check.sh: Ruff, Mypy, 457 passed
• node --check for app.js and both mjs modules
• uv lock --check
• uvx pip-audit: no known vulnerabilities
• independent final review: no blocking HIGH/MEDIUM findings