### Website or app

https://lcdev.shaped.ca

### Repro steps

Dev tools not working in FF or Chrome, says "This page doesn't appear to be using react".

React is included via CDN as shown on react website https://reactjs.org/docs/cdn-links.html:
``
	<script crossorigin="anonymous" src="https://unpkg.com/react@17/umd/react.development.js"></script>
``

Web Console on said page says:
``
Download the React DevTools for a better development experience: https://reactjs.org/link/react-devtools
``

### 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_
let lastDetectionResult;
window.addEventListener('message', function onMessage({data, source}) {
  if (source !== window || !data) {
    return;
  }
  switch (data.source) {
    case 'react-devtools-detector':
      lastDetectionResult = {
        hasDetectedReact: true,
        reactBuildType: data.reactBuildType,
      };
      chrome.runtime.sendMessage(lastDetectionResult);
      break;
    case 'react-devtools-extension':
      if (data.payload?.type === 'fetch-file-with-cache') {
        const url = data.payload.url;
        const reject = value => {
          chrome.runtime.sendMessage({
            source: 'react-devtools-content-script',
            payload: {
              type: 'fetch-file-with-cache-error',
              url,
              value,
            },
          });
        };
        const resolve = value => {
          chrome.runtime.sendMessage({
            source: 'react-devtools-content-script',
            payload: {