I am doing tmux + Claude but I wanted a bit more.
Firstly, I want to sandbox my agents from each other and from my hard-drive, and partition (and encrypt) secrets, so I use (and wrote) byre[0], and run a devbox with long-running agents for certain tasks. TermRover[1] is a pretty good SSH client for tmux. For a more native integration I have started using Happier[2] which provides a web front-end and iOS app for my sessions too (unified with real Claude Code, so handover is seamless), and put together a byre skill[3] to make that easy.
[0]: https://github.com/pjlsergeant/byre-happier-claude
[2]: https://happier.dev/