The diagnostics looked normal, but gave me a list of software to try installing. After installing about 20 programs I found the cause to be PC Reviver.
As soon as PC Reviver is installed, the Everything context menu item stops working in Opus.
If you use RegEdit to go to HKEY_CLASSES_ROOT\Directory\shellex\ContextMenuHandlers\PC Reviver and modify the (Default) value there (e.g. add not_ to the start of it) to block its shell extension from being loaded, the menu starts working again.
I don't have any experience with that one but "Cleaner" applications usually cause more problems than the solve in my experience. This one also seems to be considered malware by a few antivirus tools, although it's the first I've come across it and they may be false-positives. Malwarebytes has a detailed guide on removing it, however, and it's said to try to display ads, harm performance, and do other unwanted things, so if it was me I would probably get rid of it entirely rather than just disable the shell extension that's causing problems.