My favorite way to use tmux or et is with tabs in iTerm2.
Just moved to kitty from iterm2 a few weeks ago.
Started with alacritty, but without tab support, was a deal-breaker for me.
I use tabs in kitty with tmux on each tab.
Each tab is a context in my environment (dev/services/ansible/terraform/etc).
No. I used to use tmux extensively when I was doing a lot of remote shell work, but I don't do that any more. For local work I'd still use tmux if there was no other option, but kitty spoiled me :-).
I prefer a tab for each machine, including local, and then each tab has a tmux or ssh + tmux.