### Website or app

https://opensource.fb.com

### Repro steps

It seems that with the latest update of Chrome and React DevTools, it cannot detect pages as using React on incognito. Screenshot attached below:

<img width="518" alt="image" src="https://user-images.githubusercontent.com/34370238/235575519-8eeaa3c5-80fa-4cc4-a33d-3d2f0541f0d9.png">

* _Chrome version: 112.0.5615.137 (arm64)_
* _React DevTools version: 4.27.6 (4/20/2023)_

### How often does this bug happen?

Every time

### DevTools package (automated)

_No response_

### DevTools version (automated)

_No response_

### Error message (automated)

_No response_

### Error call stack (automated)

_No response_

### Error component stack (automated)

_No response_

### GitHub query string (automated)

_No response_
one.onMessage.removeListener(lOne);
    two.onMessage.removeListener(lTwo);
    one.disconnect();
    two.disconnect();
    
    ports[tabId] = null;
  }
  one.onDisconnect.addListener(shutdown);
  two.onDisconnect.addListener(shutdown);
}
function setIconAndPopup(reactBuildType, tabId) {
  const action = IS_FIREFOX ? chrome.browserAction : chrome.action;
  action.setIcon({
    tabId: tabId,
    path: {
      '16': chrome.runtime.getURL(`icons/16-${reactBuildType}.png`),
      '32': chrome.runtime.getURL(`icons/32-${reactBuildType}.png`),
      '48': chrome.runtime.getURL(`icons/48-${reactBuildType}.png`),
      '128': chrome.runtime.getURL(`icons/128-${reactBuildType}.png`),
    },
  });
  action.setPopup({
    tabId: tabId,
    popup: chrome.runtime.getURL(`popups/${reactBuildType}.html`),
  });
}
function isRestrictedBrowserPage(url) {
  return !url || new URL(url).protocol === 'chrome:';
}
function checkAndHandleRestrictedPageIfSo(tab) {