Background is not visible in MacBook Air

Ok, both of those look normal.

Try booting into Safe Mode to see if the issue still exists.

Try running Disk Utility First Aid on the hidden Container. Within Disk Utility you may need to click "View" and select "Show All Devices" before the hidden Container appears on the left pane of Disk Utility. Even if the First Aid summary says everything is "Ok", click "Show Details" and scroll through the report to see if any unfixed errors are listed. If there are errors, then run First Aid again until the errors are gone. If after several scans the errors remain, then you will need to run First Aid while booted into Recovery Mode.

Unless someone else has a better idea, I think the next easiest option would be to restore (aka "Migrate") your home user folder from a Time Machine backup assuming you have enough Free storage space on your internal drive. This will require either having Migration Assistant delete the current user account (it can be retained for the data), or by renaming the account you are migrating from backup. Of course you will need to restore from a backup made before this issue occurred.

I'm not an expert with Time Machine so if you have questions about it, then I will need to leave it to other more experienced contributors to assist you.

Launch the Terminal app and run the following commands so I can view the permissions associated with the home Library folder and the "~/Library/Preferences" folder as well (best to copy & paste it):

sudo  ls  -hled@  ~/Library

sudo  ls  -hled@  ~/Library/Preferences

These commands will prompt you for your admin user password. Nothing will appear on the screen as you type the password. Press the "Return" key to submit the password. Post the complete results here. I suspect you have a permissions issue since I have seen it occur several times with my organization's Macs and even a couple of posts on this forum. These commands will show me the permissions associated with those two folders.