Chrome MCP: No way to pin browser automation to a specific device (cross-device competing consumer)

Problem

When Chrome with the Claude in Chrome extension is installed on two machines under the same account (e.g., a development laptop and a headless Mac Mini running scheduled tasks), there is no way to control which device handles browser automation requests. The extension uses a competing consumer pattern -- whichever device picks up the request first wins.

This causes scheduled tasks configured on a headless server to unexpectedly run browser automation on a developer's laptop, because both Chrome instances are registered under the same account.

Reproduction

1. Install Claude in Chrome on two machines (Machine A: headless server for scheduled tasks, Machine B: development laptop)
2. Configure a scheduled task on Machine A that requires browser automation (e.g., daily social media engagement)
3. Have Chrome open on both machines
4. The scheduled task may route to Machine B instead of Machine A, with no way to predict or control which device handles it

Current workaround

Physically disable/uninstall the Chrome extension on the device you don't want handling automations. This works but is heavy-handed -- you lose the ability to use Claude in Chrome interactively on your development machine.

Requested solution

A way to pin browser automation to a specific device. Possible approaches:

• Device-level MCP toggle: Allow disabling the Chrome MCP connection in Claude Code settings without removing the extension (so interactive Chrome use is still possible)
• Task-level device affinity: Let scheduled tasks specify which device's browser to target
• Named browser endpoints: Allow naming Chrome extension instances so tasks can reference a specific one

Related issues

• #35825 -- requests global disable of Claude in Chrome
• #39637 -- multiple --chrome sessions competing for the same browser
• #39558 -- focus-stealing during concurrent browser tasks
• #20943 -- Claude Code and Claude Desktop conflict over Chrome extension

Environment

• Two Apple Silicon Macs (MacBook Pro + Mac Mini) under the same Anthropic account
• Claude Code Desktop running scheduled tasks on Mac Mini
• Claude Code CLI on MacBook Pro for interactive development