[CI] - Rethink integration testing strategy

[dev-dull]

Currently, the CI has a number of steps in CI that perform some lightweight integration tests which all report to GITHUB_STEP_SUMMARY on success. This strategy should be retooled so that failures are also reported. See linked comment below, but I think that there must be a testing framework that solves this problem in a more elegant way than just-a-bunch-of-shell-scripts™️

https://github.com/dev-dull/PyTerraBackTyl/blob/3f2e78138f356eb31e83c51e254c048fe8c3da45/.github/workflows/docker-build.yaml#L109-L111.