Both lib_joomla.ini files should be exactly the same, so the string should also be added in admin for sure. At the same time would be good to compare these 2 files for other similar issues.

If the string can't be found in admin, it is fetched form frontend (this was done in the past to let TTs make "site-only packs").

The code is present in the loadLibraryLanguage() method in SiteApplication but not in CMSApplication. I suggest to also add the same conditional there but reversing the order of priorities (admin first).

Would you consider doing a PR for it since you have better understanding of it than I do? Thanks.

Ok, will do asap.

To test I may need to obtain the same error you got as I first want to modify CMSApplication.
What exactly did you try to install. I tried with both patchtester 4.0 and 3.0 and did not get any error.

Install PatchTester 3.0.
Delete configuration.php.
Reinstall Joomla.
Reinstall PatchTester 3.0.
Got the error/warning.

Ok. Got the error.
In fact, it is just missing in backend. No need to load site one.
If a language has no admin lib_joomla.ini, it will use the en-GB one.
But both lib are not in sync and alpha order is not respected.
Making patch for that.

Please test
#27204