Add a github action that runs on each push. Since it uses the most recent docker image as the base, the runtime is relatively short with about 2h. The idea is to get quick feedback on PRs without the need to wait until the patchbot picks it up. After this ticket is merged, we can add a badge in the ticket similar to the linter workflow.

Example run: https://github.com/sagemath/sagetrac-mirror/actions/workflows/build.yml
(it works but one doctest and the pytests are failing; I think there are already tickets for these issues)

Depends on #33103

CC: @mkoeppe @fchapoton

Component: build

Author: Tobias Diez

Branch/Commit: 6329816

Reviewer: Matthias Koeppe

Issue created by migration from https://trac.sagemath.org/ticket/33263