MacBook Air login screen wallpaper not changing with the desktop.

unfortunately, some users have your same issue even when all settings are set properly for what you want to achieve.

I would recommend trying to Start up your Mac in safe mode. run the Mac is safe mode for about 5 minutes, then restart your Mac normally and see if it is corrected. sometimes a safe boot followed by a normal boot can clear up some anomalies.

and then, I need to ask, are you using any apps that claim to "clean up" or "speed up" or otherwise "optimize" your Mac? and / or any antivirus apps? the only thing those apps are good for is causing major issues within macOS while providing ZERO protection or benefit. you would do well to uninstall them.

if you have no such apps, i'm thinking you should download and run the free version of EtreCheck so we can see if you have some software installed that is causing your issue. make sure you give "full disk access" to etrecheck. Learn how to use it by reading Using EtreCheck. if you need help interpreting the report, you can see how to post the report here by reading How to use the Add Text Feature When Posting Large Amounts of Text, i.e. an Etrecheck Report. and it automatically obscures sensitive things (like serial numbers) so you don't have to worry about sharing the report here.

the only thing I saw was App Cleaner. that is apparently the least problematic app in that category of apps. but if it were my Mac, I would still uninstall it.

but even if you do uninstall it, there is no guarantee that you will get the matching login window you are hoping for. though not common, there are a few users that cannot get it to work. the only thing I can say is "how long do you have to look at that screen?"