GitHub Actions uses the Ghost API, not git, to push your changes to your site.
The reason this is better than using git is, Ghost’s API knows how to refresh the internals of your site so that your theme changes are all accurately reflected.
So this part of your work:
git clone <repo URL> in
/var/www/ghost/content/themes and noted the directory existed now, and all the content is the same as it appears on Github.
Was totally unnecessary. If you used this kind of git workflow, then every time you push a change to GitHub you’d then need to login to your server, go to this folder, run
git pull and then restart Ghost. That’s a lot of steps.
Instead, what you need to do is push your changes to the master branch and then look at the “Actions” tab in GitHub to see if the build ran successfully.
If it did not run successfully, you will need to troubleshoot the errors in your Action first.
If/once it has run successfully, login to Ghost Admin and look at the theme list. The GitHub Action may have pushed your theme with a new name. If it did, you’ll need to activate that theme.
Once you’ve got that working successfully once, push a second change. This time the changes should be picked up without any additional work from you.