[FEATURE] Enable claude code desktop to start multiple new chats from remote

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

In order to enable remote control, you first need to start a new chat on your local computer and then enable remote control on the conversation so it can be connected from the phone app.

Limitations:

1. You can only start a new chat by first creating it on your computer
2. On the go, you are limited to only sessions that you have already started, and remote-control is enabled on your local computer.

Proposed Solution

The desktop app should start a remote session that can be accessed by the phone app, where the user can start as many new chats as desired. Instead of remote controlling a chat, you remote control the Claude desktop app.

This is a functionality that is currently offered on the Codex app. We want to achieve the same behaviour here.

Priority

High - Significant impact on productivity

Feature Category

Developer tools/SDK

Use Case Example

Common developer scenario:

1. I'm on the go (on my phone) working on a chat session that I initiated on my local computer.
2. The session quality starts to deteriorate and/or I want to shift the topic of the conversation to something different (bug fix, investigation, PR review, or new feature development).
3. Starting from my phone (Claude iPhone app), a new remote conversation that gets executed on my remote computer, where I compile and test my project, is impossible.

With this feature, I would be able to ship more high-quality work on the go by starting fresh chats as needed. Additionally, this would allow the user to start as many sessions on their phone as needed.