### 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_
const id = tab.id;
    
    
    if (request.hasDetectedReact) {
      setIconAndPopup(request.reactBuildType, id);
    } else {
      const devtools = ports[id]?.devtools;
      switch (request.payload?.type) {
        case 'fetch-file-with-cache-complete':
        case 'fetch-file-with-cache-error':
          
          devtools?.postMessage(request);
          break;
        
        case 'react-devtools-required-backends':
          const backendsToDownload = [];
          request.payload.versions.forEach(version => {
            if (EXTENSION_CONTAINED_VERSIONS.includes(version)) {
              if (!IS_FIREFOX) {
                
                chrome.scripting.executeScript({
                  target: {tabId: id},
                  files: [`/build/react_devtools_backend_${version}.js`],
                  world: chrome.scripting.ExecutionWorld.MAIN,
                });
              }
            } else {
              backendsToDownload.push(version);
            }
          });