Hello.
I can confirm your error. I updated Elemetor to the latest version 3.25.0 an hour ago and wanted to import a template from ‘My templates’. This always created an error message:
The following error(s) occurred: You do not have permission to access this template
First I thought the problem was the template itself but I had imported the same one a few weeks ago with no problem. To test this, I then saved a part of a webpage as a template and tried to import that one on another page – same issue and error.
This Elementor update surely has a bug and that is that you cannot import any own templates anymore.
I then found the solution to rollback to the previous Elementor version, in this case 3.24.7 and the import worked again with all templates.
So the problem is clearly the update.
I presume if I update now again to the latest version all templates will stay on the respective pages, just the import function needs to be fixed.