Mac mini M1 2020 w/ Monterey, Parallels & Win 11.

Parallels installs a driver into macOS to function properly. The upgrade from Monterey to Ventura may whack that driver, or it may not.

Parallel's 19.40 was just released and I think that if you check for Parallel's updates from the application after the Ventura upgrade, it will show that 19.40 is available, and attempt to reinstall a newer driver. To do that, it will prompt you to open System Settings > Privacy & Security (just click that button on the Parallel's dialog that appears, and with your admin password, allow Parallel's. It will then reboot your Mac, and you should be good to go.

The Ventura System Preferences were renamed to Settings and Apple played musical chairs with the Preferences organization. You will be mumbling about that for quite some time…

never heard about any apps on macOS which required a reinstall when one updates macOS version before,

apart from when apps becomes incompatible like with catalina not being able to run 32bit apps, so while I've never used parallels I would assume you would not be required to

If you are moving from an Intel Mac to an M-series Mac, then you won't be able to use your Intel version of Windows VM. You need to use an ARM version of Windows on an M-series Mac. I don't know whether there is any way to transfer a Windows configuration & setup to another platform.

I get the impression that the OP is asking about upgrading a M1 Mac mini from Monterey to Ventura – not about migrating from an Intel-based Mac to an ARM-based one.