I'm asking for help with FileVault enabled.
A similar question was answered for Mojave, but their Swift program doesn't work in Big Sur because
/Library/Desktop Pictures/Mojave.heic no longer exists.
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The background of the login screen is in this location
/Library/Caches/Desktop\ Pictures/<a specific string>/lockscreen.png
If only one user is registered on your system, you will see a folder with a picture that is displayed on your lock screen and one from the system for which you first need higher rights to view it.
The lock screen folder of the system is there so that if, for example, several people are registered and just want to log in, this image then appears for everyone. The system doesn't know exactly who wants to log in, so there is a lock screen for everyone first. But if the user has clicked on his profile and wants to enter his password, he will see his lock screen again.
By the specific string, I literally mean the UUID, which you can look up:
Go to System Preferences >
Users & Groups >
Your Account >
Right Click (Advanced Options) >
Now you will see your UUID