New `chrome://inspect/#remote-debugging` "Allow remote debugging?" popup can trigger multiple times and stack up

Description of the bug

Currently when connecting to a live browser using the new v144+ chrome://inspect/#remote-debugging --auto-connect feature, the "Allow remote debugging?" popup can trigger multiple times and stack up, which looks like a bug to users as they have to click "Allow"/"Deny" multiple times to fully dismiss them.

Reproduction

1. Connect to a live chrome instance by sending the user to chrome://inspect/#remote-debugging
2. chrome-devtools-mcp/puppeteer/stagehand/browser-use/etc. clients may poll :9222 trying to connect until it's ready, or multiple subprocesses may try to connect in parallel
3. Multiple poll attempts / reconnections from the drivers each trigger their own popup in the browser
4. The user has to click "Approve"/"Deny" several times to dismiss the stacked popups, which looks like a bug

Expectation

Ideally only one popup is shown at the start on initial CDP connection, then multiple processes should be able to connect without triggering subsequent popups. This allows driver libraries to reconnect automatically on crashes or to make multiple CDP connections in parallel if their architecture requires it (e.g. some AI browser tools use separate subprocesses to do different things, or to run multiple sub-agents that all connect to chrome, or sanboxed agents may resume from a snapshot and attempt to reconnect to the existing CDP endpoint).

If chrome team decides they must show a separate popup for every unique CDP client connection, then the UI should at least differentiate them as separate requests and show something like "<xyz> client is trying to connect from<clientip:srcport>..." so that users don't just think it's a buggy prompt that isn't registering their clicks.

MCP configuration

--auto-connect

Chrome DevTools MCP version

0.21.0

Chrome version

144

Coding agent version

NA

Model version

NA

Chat log

NA

Node version

25

Operating system

macOS

Extra checklist

• I want to provide a PR to fix this bug

Start by tracing the --auto-connect flow from chrome://inspect/#remote-debugging through the :9222 connection and reconnection handling. Reproduce parallel polling or multiple CDP connections, then verify that repeated attempts no longer stack duplicate "Allow remote debugging?" popups while legitimate connections continue to work.