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).