Does reinstalling the Mac operating system erase your data?

Hello, HFB.

No, reinstalling the macOS does not have to erase you data.

if all goes well, the only time that should happen is when you choose to Erase, Format, or Partition your drive using Disk Utility. That is not required when you simply wish to reinstall the OS.

But always good advice above from Jack-19 about having backup.

Backup your Mac with Time Machine - Apple Support

Welcome to Apple Support Communities.

It should not, but you need to have a backup first in case something happens!

Jack