feat: drive Claude Code via Claude Agent SDK instead of CLI subprocess - #10

Node.js 20 is deprecated. The following actions target Node.js 20 but are being forced to run on Node.js 24: actions/checkout@v4, docker/build-push-action@v5, docker/login-action@v3, docker/metadata-action@v5, docker/setup-buildx-action@v3, docker/setup-qemu-action@v3. For more information see: https://github.blog/changelog/2025-09-19-deprecation-of-node-20-on-github-actions-runners/