Not tab, shift-control-right/left arrow for switching tabs in Safari. That does not work but that is what shows in the menu. What works is shift-COMMAND-arrow key.
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.
I often imagine engineers sitting on a beach having a drink and comparing notes about what they’ve done to users in the past.
Engineer 1:
When I worked on Safari, I made the next tab shortcut control + tab! lol
And get this - previous tab is control + shift + tab!! Muwahahaha
Engineer 2:
Wow, that’s awesome! I’ve put a number of support structures in front of screws that people need to remove during servicing equipment, but nothing as devious as that!