So from what I can understand this is only meant to be used with Claude-hosted sandbox environments?

Wouldn't work for my case since I need a lot of HDD space, GPUs etc. to run the thing I'm working on, but it would be great if I could run a Claude Code server in my server, expose the port and then connect via web or iOS interface.

Sure I can use tmux/ssh but it's very impractical specially in mobile.