actions: Do not run tests on push to main

[olix0r]

Each time we push to the main branch, we run a full set of unit and
integration tests, even though the branch has already passed CI before
merging. When we have many branches in-flight, this work chews into our
actions usage, delaying actions for open PRs that are more important to
run expediently.

This change disables running these tests on push to main. We continue
to run CodeQL checks on main, as these checks appear to be necessary.

[olix0r]

Note that this failure there isn't even a true failure -- there was an error pulling the Debian docker image.

[alpeb]

One thing that the CI failure in #6873 promptly reminded me is that all the docker layer caches are rooted at the caches generated in the main branch (see the docs for a detailed description). This vastly speeds up builds in PRs, even external ones. So at a minimum, I think we should keep on building the images in main.