Do you have an older version of MC still installed on the second PC?
If so the Windows File Association may still be pointing back to the older version for the mjr file type. You can fix that. You can also check that very easily by double-clicking on the mjr file, then when the "Do you want to allow this app to make changes to your device" message pops up, click the "Show more details" link. You will be able to see from the path to the "PackageInstaller.exe" file whether it is trying to run the MC23 version, or some other version.
If this is the issue, type "Default app settings" in the Windows menu search field, and press enter. Then click the "Choose default apps by file type" link, and scroll down to the mjr file type. You will see that it is assigned to the "Package Installer" app, but unfortunately, it doesn't identify which version of MC that Package Installer belongs to, and if you click on the Package Installer icon, you will probably see two or more Package Installers listed. Windows also doesn't highlight which Package Installer is currently associated with the mjr file type.
So the only way I have found to check if the correct installer is associated with the mjr file type is to click the first "Package Installer" in the list, let it update (a couple of seconds), and then double-click on the mjr file again and select "Show more details" to see which installer it is pointed at. If it is still pointing at an earlier version that MC23, go back and select the second "Package Installer" in the list and check again.
Once the mjr file is associated with the correct MC23 Package Installer, click on the Yes button to complete the licence installation.
Yes, MC should have changed all the file associations when you installed MC23. No, it doesn't always work.
Yes, it would be nice if the Package Installer name included the MC version it was associated with. I might put in a request for that. EDIT: Done.
https://yabb.jriver.com/interact/index.php/topic,112049.msg794448.html#msg794448You may want to check other file associations are pointing to MC23 rather than an earlier version.
Let us know if this fixes the issue.