If you're on a Mac, try tmux -CC with iTerm2. You get tmux goodness like multiple panes, persistent sessions, etc. But you also get native scrolling, native copy and paste, etc. It's what makes tmux usable for me.
Tmux + iTerm2 is a fantastic combo that takes all of Tmux's pwer and removes all the downsides.
I searched if anything else used Tmux's Control Channel on Linux to replicate iTerm2's features, and I'm sad that I found nothing.
(Frankly, it's kind of stunning to me that one terminal app on macOS has more useful features than the plethora of me-too terminals on Linux)
If by "useful features" you mean intercepting tmux output and having it integrate with the terminal, then no. But more generally, I think the closest thing to iTerm2 on Linux is Tilix [1].
Such an enormously usable thing, why isn't that readily available on Linux?
So much of it is lost because work machines have been either windows or Ubuntu. I tried a few things but nothing comes even close to the level of overview and speed you have with iterm. In the end I usually end up using multiple windows and too much mouse..
The tmux integration is just the cherry on top
Alternatively, there's apparently a forked version of mosh out there with iterm2 support hacked in, but I've not tried it.
Unfortunately.