The behaviour you describe sounds frustrating, particularly as clicking files in Finder's Column view does not highlight them, while pressing the right-arrow key restores the expected selection.
The fact that shortcuts in Favourites work normally is an interesting clue.
I would start by testing a few different folders and switching to List view (View >> as List) to see whether the problem is specific to Column view.
Then relaunch Finder by holding Option and right-clicking its Dock icon and choosing Relaunch.
If the problem persists, try using a different mouse or trackpad, and test Finder in a temporary macOS user account.
If it works there, something in your usual account may be responsible
if not, a system-wide issue becomes more likely.
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Check your exact macOS version under Apple menu >> About This Mac, and see whether an update is available under System Settings >> General >> Software Update. Apple's guide is here: Update macOS on Mac.
If the problem persists across folders and user accounts, I might report it to Apple. Include the steps needed to reproduce it and, if possible, a short screen recording showing the missing highlight and the right-arrow workaround.
You can find Apple's guidance here:Feedback Assistant.
Given that keyboard navigation works but mouse selection appears not to, I think it is ’worth investigating further rather than assuming you are doing anything wrong.