Test workflows appear not to run on push to `main`

When I go to the main page of the repo and click on the green tick for CI, I can see that the pre-commit workflow has run, but seemingly none of the others (e.g. the ones that test the templates).

No idea why this is happening, because all the relevant workflows appear to have `on: push: branches: [main]` set.

Start by inspecting the GitHub Actions workflow definitions, comparing the pre-commit workflow with the workflows that test the templates and their push-to-main triggers. Reproduce the behavior from the repository’s CI page and trace why only pre-commit runs. Done means the relevant template-testing workflows run on pushes to main as intended.

Written by the indexing model from the issue text.