It's technically possible, but not the best idea, involves modifying the EFIRES file in the Preboot volume containing the login ui elements, fittingly named loginui.efires, but I don't recommend doing this at all but there is a way. If you do this in recovery, because you can't mount the Preboot volume RW on the OS, and the currently mounted Preboot volume in recovery is the recovery Preboot, so you have to mount the os one, unpack the fires, change the background png, and probably also the buttons because they may be purplish if apple decided to make them look like that on your macOS version. (Monterey) ANY MAJOR OS upgrade, MAYBE not a minor upgrade, but an upgrade like Monterey to Ventura will revert your changes to the background, and will require you to recopy over your modified EFIRES file to the preboot volume. The path would be for the EFIRES file: (Preboot Mount Point)/(A UUID, probably specific to you)/System/Library/Caches/com.apple.corestorage/EFILoginLocalization/loginui.efires
A Better way to do this would to be to replace the EFIRES file at /usr/standalone/i386/EfiLoginUI/loginui.efires, but requires a SIP disable, albeit temporarily, but allows modifying the file in the OS while SIP is disabled. Anywaybye