No, there is no limitation on third party fonts. Though if the font you installed conflicts with a system font, that will cause odd problems (in any OS).
Font Book is, and always has been a flakey app (it's much improved in Ventura). Fonts you know are active but don't appear in your apps, or only some apps, is a pretty common problem when using Font Book.
Try resetting Font Book. Note that you will lose any Collections or Library sets you've created.
To reset Font Book completely, do the following in the order listed. It takes the least amount of time and only two restarts.
1) Quit Font Book. Open the Preferences folder in your user account and put the following two files in the trash.
com.apple.FontBook.plist (does not exist in Ventura)
com.apple.FontRegistry.user.plist
The file com.apple.FontBook.plist keeps track of Font Book’s general preferences and activated fonts, whether as a standard or library collection. The file com.apple.FontRegistry.user.plist keeps track of deactivated fonts. Both may not be present. Delete what’s there.
2) Open Terminal and enter the following command (for Big Sur and earlier, only):
sudo atsutil databases -remove
Enter your administrator password when prompted. This removes all font cache files maintained by macOS.
For Monterey or later, use this command:
atsutil databases -removeUser
This removes all font cache files of the currently logged in user account.
3) Restart your Mac and immediately hold down the Shift key to boot into Safe Mode. Keep holding the Shift key until macOS asks you to log in to your user account (you will get this screen on a Safe Mode boot even if your Mac is set to automatically log in). Let the Mac finish booting to the desktop and then restart normally. This will clear the remainder of Font Book’s database and the cache files for the user account you logged into in Safe Mode.
Now try adding your third party fonts again and testing in Photoshop to see if they appear as expected.
