Are you implying you have a solution to sync the X selection buffer and the X clipboard?
When I yank to the "kakoune clipboard buffer" in kakoune (a terminal text editor), the X clipboard is updated (again through OSC 52). When I copy something to the X clipboard (either on chrome or some other program), the "kakoune clipboard buffer" is updated [0].
[0]: technically, the kakoune clipboard buffer updates itself from the X clipboard when it is read from.