I can confirm this problem. I had to save the template.json file under a different filename (template_new.json) to make my changes to be picked up. Clearing the cache (drush -cr) did not help.
But now when I add another change to the new file - it works as expected! Even without clearing the cache.
But when I select the file with the old filename again, I still get the old content of the file although the content of both files is identical!
Very strange.
I applied the patch #3 ✨ Provide option to display contextual links on embedded entities Needs work successfully (Drupal 10.1).
👏 Thank you @xaqrox! This is an important UI improvement for my use cases.
I can confirm that this problem still exists in version 2.0.0-rc1.