Feature Request: Web App #260

Cool app but needs to be liberated from the Desktop app. Should be a web app with a rust web server. This would allow:

• Remote access to the web ui from my phone while I'm away from my desk.
• I can only manage Claude Code on my host machine, but can't manage Claude Code running inside my VMs.
• I'm sure there are other benefits.

Without any knowledge I got pretty close to making this work, I had the app running in a web app and separated the Tauri stuff into an api server but gave up after a few hours do to my limited Rust experience.