You can just install Claude Code on the server and drive it from Claude Desktop via remote control. That way you can control Claude Code on mutiple servers straight from your Claude Desktop, Mobile or Web, and stay fully within Anthropic tools.

Everything works: you get the native view of subagents, you can upload files and images, fork threads, etc.

The massive upside is that the actual work happens on the server so you can close your laptop and it will continue plus it will not fry your thighs. The advantage over sessions (which I haven't tried but theoretically sound) is that you can configure Claude's environment on the server however you like. Give it any tools you need, ssh access to other machines, sudo, whatever.

The only downside is that every new project requires a setup step on the server (to add the systemd service) where you will develop it since Claude can only handle one server per directory. Claude will handle this step however if you give it ssh access to your server.

The machines show up nicely in Claude Desktop/Mobile/Web, and repos/projects are in a dropdown. Unless you work on very many projects at the same time, this setup is golden.