What would change?

Add a GitHub Actions workflow that regularly runscheck_versions.py, and use the "job summary" feature to make that visible in a more prominent location. This would allow linking to the workflow's page from the README, where the user can click into one of the jobs and see the version table as a "job summary".

https://docs.github.com/en/actions/using-workflows/workflow-commands-for-github-actions#adding-a-job-summary

The link from the README would be similar tothis one for pypi-package.yml, and the job summary would be a markdown block presented likeBuild & verify package summary (this example uses<details> for dropdowns, and also attaches artifacts which are shown above the summary -- we likely wouldn't do either of those things).

What is the benefit of this?

This would eliminate the need for follow up bump PRs like#156 in the future, since the information would be automatically tracked and kept up to date via the regular re-runs of the script (with historical information as well, which is a nice side-effect?).