test: verify Docker image builds and starts successfully

[icebear0828]

Fixes #120. Adds a new GitHub Actions workflow to build the Docker image and verify that the container starts correctly, waits for the healthcheck to pass, and can be curled on both the default port (8080) and a custom overridden port (8090). Cleanup is handled properly.

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PR created automatically by Jules for task 15203459648414769429 started by @icebear0828

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