We can do this through https://docs.github.com/en/actions/writing-workflows/choosing-where-your-workflow-runs/running-jobs-in-a-container, and it is less painful to make both image environments the same.

See: #122566 (review)
cc @erlend-aasland @hugovk @Damien-Chen

Linked PRs

• gh-125741: Update check_generated_files CI to use our published container image #125744
• [3.13] gh-125741: Update check_generated_files CI to use our published container image (gh-125744) #125759
• [3.12] gh-125741: Update check_generated_files CI to use our published container image (gh-125744) #125760
• gh-125741: Update build.yml for the new check_autoconf_regen job #125772
• [3.13] gh-125741: Update build.yml for the new check_autoconf_regen job (GH-125772) #125779
• [3.12] gh-125741: Update build.yml for the new check_autoconf_regen job (GH-125772) #130229