What is this called and how do I remove it?
Not ours - in desktop Windows anyway. Are you using a Windows 10 phone perhaps?
On desktop versions there would be a context menu available with those and other options, though I suppose on a phone it might look different. As in, they may simplify the menu so it will fit your screen and be touch-clickable.
Do you have any extension for text highlighting / searching etc
this looks like an extension...
open opera://extensions/ and look for it
you can also test in private window text selection, and see if it happens
because extensions won't work in private windows by default (unless explicitly enabled for private windows)
Uninstalled and reinstalled the browser. That fixed it.