According to StackBlitz synchronization with github - upload to from StackBlitz to github it is possible to commit from Stackblitz to Github.
But when I tried it doesn't seem to do so. When I checked Github Repo I still have my old Readme compared to the new one:
If you have linked to a github repo and made changes locally in the editor, you should see a button on the top right to Commit your local changes
Which should pull up a dialog allow you to Commit and Push
After which you should see a successful toast
If any of these aren't working, it's possible there was a bug at the time you tried it, but appears to have been resolved as of June 2023