Add GitHub Actions job that runs the tests in an installed Python

[FFY00]

Feature or enhancement

Proposal:

Ugh, I have tripped into this again... I have a PR with all the tests green on Github, but the Python installation is pretty much broken because I forgot to update something on the build system.

My latest example is GH-110785, which causes the sysconfig module to be missing after installing. The breakage was caught by the buildbots, which is good, but we should not be able to merge something into main that causes such major breakage, and still, I don't feel very confident with only two buildbots failing.

I think we should have a job on Github that installs Python and runs the tests using that installation.

Has this already been discussed elsewhere?

This is a minor feature, which does not need previous discussion elsewhere

Links to previous discussion of this feature:

No response

Linked PRs

• GH-110793: add GitHub Actions job that runs tests after installing #110794