When the Mac boots it is using the read-only unencrypted SSV (signed system volume) which is the same on all Macs. This has no customisation.
Your login password is required to unlock and mount the read/write part of the boot volume where your wallpaper resides. So you have to login before the background image can change. So everyone has the same background image before login. You can't change it.
Most people find that annoying unless they really like the login picture/graphic. Is is one of the compromises we have to make to get Apple security features.
The only way round this is to break the SSV and, in recovery, mount it R/W and make changes. Not sure if this can work with Apple silicon - maybe only Intel. This is not good practice as it destroys much of the security barrier which Apple has put around macOS. Also makes macOS updates a bit tricky. Don't ask!
I generally only boot my Macs for macOS updates, so that avoids much of the annoyance.
Ps. I understand the image is of some Sequoia trees.