[FEATURE] Allow slash command usage over remote-control

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet
• [x] This is a single feature request (not multiple features)

Problem Statement

While the remote-control feature is very nice and much appreciated, I think allowing the use of slash commands through the remote-control connection would be a great improvement. They don't seem to work, currently.

Proposed Solution

I'd like to be able to use commands such as /clear, /compact, etc. over the remote-control connection.

Alternative Solutions

As an alternative, I've previously used Happy to control claude sessions remotely with some success but having a solution directly from anthropic is preferable.

Priority

Medium - Would be very helpful

Feature Category

CLI commands and flags

Use Case Example

Let's say i'm working on a project and want to change the model, or compact at a certain time, or clear the context. Being able to use a slash command like we can in the CLI would be nice.

Additional Context

_No response_