How to keep the Dock visible on a iMac?

The advice you have been given by 6x6 and BDAqua is spot on.

If you DEactivate "Automatically hide and show the Dock", it should be permanently visible.

Since this appears not to be working as expected, do start in Safe Mode.

Please confirm whether things are working as expected while you are in Safe Mode.

If it is not correct even in Safe Mode, then maybe deleting the plist file could help (but would restore the Dock to its default state).

If it is correct in Safe Mode, restart normally and see if it got fixed. Let us know.

Start with this...

Safe Boot, (holding Shift key down at startup), does the problem occur in Safe Mode? Could take 10 minutes or more.

Safe mode attempts to repair Disks & clears lots of caches & loads safe Drivers, & prevents loading of 3rd party extensions, so if Safe Mode works try again in regular boot.

To find out if it's system wide or user specific, try this...

Open System Preferences>Users & Groups, unlock the lock, click on the little plus icon, make a new admin account, log out & into the new account.

Does it work in the new account?

Go to System Preferences > Dock & Menu Bar and deactivate "Automatically hide and show the Dock."