tmux is great, specially when you need persistence in a remote server where you don't want or can't install any other software, and when you are stuck with some 2010 terminal emulator.

But if you have control over your setup, I would use a capable terminal and ditch in-band multiplexers that sit in the middle of the process and your terminal eating up escape sequences and native features while adding latency. Then use a separate tool for session persistence (I like zmx but there are more for this).