[Feature Request] Add multiplexer mode to handle concurrent tab operations

Feature Request
Design the Claude --chrome extension as a multiplexer to handle multiple tabs at once.

Environment Info

• Platform: darwin
• Terminal: intellij
• Version: 2.1.12
• Feedback ID: 50c81985-4211-466e-9f74-b1f09980abb0

My session:
Can I run more than one claude --chrome session and integration at once?

⏺ claude-code-guide(Check claude --chrome multiple sessions)
⎿  Done (2 tool uses · 24.1k tokens · 14s)

⏺ Not officially documented, but there are likely practical limitations:

The constraint: The Claude in Chrome extension runs as a single instance per browser. Multiple Claude Code processes trying to send commands to the same extension would likely conflict.

Practical options:
┌─────────────────────────────────────────────────────┬─────────────────────────────────────────────────────┐
│ Approach │ Works? │
├─────────────────────────────────────────────────────┼─────────────────────────────────────────────────────┤
│ Multiple claude sessions (no --chrome) │ Yes │
├─────────────────────────────────────────────────────┼─────────────────────────────────────────────────────┤
│ Multiple claude --chrome → same Chrome window │ Probably not - extension contention │
├─────────────────────────────────────────────────────┼─────────────────────────────────────────────────────┤
│ Multiple claude --chrome → separate Chrome profiles │ Maybe - each profile has its own extension instance │
├─────────────────────────────────────────────────────┼─────────────────────────────────────────────────────┤
│ One --chrome session + other non-chrome sessions │ Yes │
└─────────────────────────────────────────────────────┴─────────────────────────────────────────────────────┘
If you need parallel browser automation, you could try running separate Chrome user profiles (each with the extension installed), but this isn't a tested configuration.

For your worktree setup, you could have multiple Claude sessions running on different worktrees, but only one using --chrome at a time.

✻ Baked for 38s

❯ But you could potentially design the extension to broker multiple tabs to multiple sessions, right?

⏺ Yes, absolutely. The extension could act as a multiplexer:

┌──────────────┐ ┌──────────────┐ ┌──────────────┐
│ Claude CLI 1 │ │ Claude CLI 2 │ │ Claude CLI 3 │
└──────┬───────┘ └──────┬───────┘ └──────┬───────┘
│ │ │
│ Native Messaging │ │
└────────────┬───────┴────────────────────┘
│
┌────────▼────────┐
│ Chrome Extension│
│ (Session Broker) │
│ │
│ Session Map: │
│ CLI-1 → Tab 4,5 │
│ CLI-2 → Tab 7 │
│ CLI-3 → Tab 9 │
└────────┬─────────┘
│
┌────────────┼────────────┐
│ │ │
┌───▼───┐ ┌───▼───┐ ┌───▼───┐
│ Tab 4 │ │ Tab 7 │ │ Tab 9 │
└───────┘ └───────┘ └───────┘

Design would need:

1. Session registration - CLI connects and gets a session ID
2. Tab ownership - Each tab tracked to its owning session
3. Command routing - Session ID attached to all commands
4. Event routing - Tab events dispatched to correct session
5. Session cleanup - Release tabs when CLI disconnects

This is similar to how Chrome DevTools Protocol (CDP) works - Playwright and Puppeteer both support multiple browser contexts with isolated tabs through a single connection.