Exactly which MacBook Air model and year is this computer?
Native resolution for the
In this last pic of yours, the default resolution choice will be the icon on the right with the gray outline, which I suppose is not selectable?
In your original post you stated that you ❝tried to change resolution with different software❞.
So what, exactly, was that other software?
Are you running any anti-virus, cleaning, optimizing or VPN software?
If so, you should disable and/or uninstall that as these type of apps and utilities do often interfere with the proper operation of the OS.
I think it probably best to reinstall macOS. This will not alter or erase your user files, but will simply copy a fresh set of OS files to the drive, replacing any corrupt or missing system files. However, you should backup your data just in case. How to reinstall macOS
NOTE– You should not have to delete, erase, format, partition or otherwise alter your startup disk for this. If that becomes an option, quit the process and restart your Mac. Then come back here for additional advice.