[infra] Add CI workflow job to build gateway and API Docker images

[yinkscss]

Context

CI runs fmt, clippy, and tests but never validates that production Docker images build successfully.

Problem

Dockerfile regressions (missing COPY paths, broken cargo targets) can reach main undetected until deploy time on Render.

Proposed scope

• Extend .github/workflows/ci.yml with a docker job
• Build Dockerfile.gateway and Dockerfile.api on every PR
• Fail CI if either image build fails

Acceptance criteria

• CI job builds both Docker images without cache-busting hacks
• Job runs on push to main and on pull requests
• Failed Docker build blocks merge
• Job completes in reasonable time (reuse rust-cache where possible)

References

• .github/workflows/ci.yml
• Dockerfile.gateway
• Dockerfile.api
• render.yaml