This is a big deal! (it shouldn't be, but it is)
My main complaints about vim/emacs in the past was at the sheer complexity of getting something that should not even be a concern (clipboard integration) working properly, when other text/code editors did not have this problem at all.
Searching online, it seems like tmux has some nice documentation related to OSC 52 usage:
https://github.com/tmux/tmux/wiki/Clipboard
I will be playing around with this for a bit to understand it more. But honestly, this is the sort of thing that should "Just Work TM".
"VTE terminals (GNOME terminal, XFCE terminal, Terminator) do not support the OSC 52 escape sequence."
https://gitlab.gnome.org/GNOME/vte/-/issues/2495
That's a shame, but I'm not against using a different terminal emulator. Up until now I did not really have a good reason to.