In Safari’s menu/Window, the shortcuts are as shown above, which shows the CONTROL key as a trigger but this doe not work for switching tabs in Safari. But, using the COMMAND key as a trigger does work.
As to keyboard shortcuts in system preferences, I think that is a different issue.
Ditto here. There’s nothing wrong with the shortcuts shown in the OP’s image.
I assume there is some other conflict on the OP’s machine that has nothing to do with Safari. Easy to check. Quit everything and boot into a different or new user account and see if Safari there behaves as expected. That’s always the first thing I do before reaching for the phone.