Where did the preference panes go to when I installed Big Sur?

Are you referring to the System Preference panes? Don't you have something like this?

If they are not showing up boot into Safe Mode by booting with the Shift key held down and check there to see if the problem persists.  Reboot normally and test again.

NOTE: Safe Mode boot can take up to 10 minutes as it's doing the following; 

• Verifies your startup disk and attempts to repair directory issues, if needed

• Loads only required kernel extensions (prevents 3rd party kernel/extensions from loading)

• Prevents Startup Items and Login Items from opening automatically

• Disables user-installed fonts 

• Deletes font caches, kernel cache, and other system cache files

I’ve used Macs for a lot of years. I don’t know what “Preference panes” might mean.

Looks like there are no user installed Prefpanes. The System Preference Panes are those that show under System Preferences. I found them under MacHD/System/Library/PreferencePanes.

Double click on those that you found and see if it won't reinstall as it should. Otherwise try my previous suggestion.

Just so we're on the same page it's the user installed pref panes that are missing, right? You may have to download and reinstall the apps that included the pref panes.

In the finder, hold down the Option key then go to the menu Go > Library and use the search bar there to search for PreferencePanes.

MtD