Mac starts up to a circle with a line through it

Apple said that it means "that your startup disk contains a Mac operating system, but it's not a version or build of macOS that your Mac can use" (https://support.apple.com/en-us/HT210901). However nothing was installed or updated, it just stopped working.

Apple recommendations are to boot in Recovery mode, and use Disk Utility to repair startup disk and if disk utility found no errors, reinstall MacOS. But what are the solutions if we don't want to reinstall but recover what we had?

In recovery mode, I can't set up a boot disk...

Why did this problem happen?