Add tests for Docker builds to GitHub Actions

**Is your feature request related to a problem or challenge? Please describe what you are trying to do.**
Bugs such as #402 that can be easily detected by Docker build tests in GitHub Actions exist.

**Describe the solution you'd like**
Add Docker build tests to GitHub Actions.

**Describe alternatives you've considered**

**Additional context**

Inspect the repository's GitHub Actions workflows and Docker build configuration, then review issue #402 to identify the failure these tests should catch. Done means Docker builds are exercised in GitHub Actions and failures are reported by the workflow.

Written by the indexing model from the issue text.