I've largely given up using tmux in favor of wezterm: wezterm has the ability to remote connect to a persistent terminal running on another machine, and has native window objects so things like mouse support and copy/paste work out of the box. It also has a kind of mosh-like support, though not quite as good at persisting connections over bad networks or network disconnections as mosh+tmux.

The down side is that it's really sensitive to versions, right now I'm struggling to get it to work on NixOS in the version that I have running on my Ubuntu dev box and MacOS laptop.