I always setup my terminals to open a tmux session by default (or attach to any existing one). For example, in my ~/.config/alacritty/alacritty.toml:

    [terminal.shell]
    args = ["-l", "-c", "tmux attach || tmux"]
    program = "/opt/homebrew/bin/zsh"

tmux supports tabs so you can have multiple Claude Code sessions running concurrently. You do need to learn a few tmux keyboard shortcuts to use it effectively (e.g. opening/closing/switching tab).

Sorry didn't answer "how important is mosh?"

Depends- how good is your signal? Mosh has a great property that it buffers everything locally so there's no lag even if your connection sucks.

On ssh, every keystroke is a roundtrip

"tmux ls" shows you all the open tmux sessions

Could even use cc to check in on and/or "send-keys"

What wasn't working about mosh? Just install mosh and use mosh to connect

I recommend Eternal Terminal instead of mosh for this.