And case in point, mosh is another terminal layer, it's also a multiplexer of sorts.

I've used mosh a lot but it's just interesting to note it's in the same category as screen and tmux

On mobile so I’m not sure which case OSC52 applies to, but I use mosh+tmux 8-10 hours a day. Both bracketed paste and tmux selection setting local clipboard work fine

it sort of does support it, except it doesn't work with tmux.