### Preflight Checklist

- [X] I have read the [Contributing Guidelines](https://github.com/electron/electron/blob/main/CONTRIBUTING.md) for this project.
- [X] I agree to follow the [Code of Conduct](https://github.com/electron/electron/blob/main/CODE_OF_CONDUCT.md) that this project adheres to.
- [X] I have searched the [issue tracker](https://www.github.com/electron/electron/issues) for a bug report that matches the one I want to file, without success.

### Electron Version

19.0.0-nightly.20220209

### What operating system are you using?

Windows

### Operating System Version

10.0.19043 Build 19043

### What arch are you using?

x64

### Last Known Working Electron version

_No response_

### Expected Behavior

1. Open DevTools->Settings->Shortcuts
2. Change "Match shortcuts from preset" to "Visual Studio Code"
3. Close devtools and reopen
4. Shortcut setting remains last selected value

### Actual Behavior

1. Open DevTools->Settings->Shortcuts
2. Change "Match shortcuts from preset" to "Visual Studio Code"
3. Close devtools and reopen
4. Shortcut setting reverts to default

### Testcase Gist URL

_No response_

### Additional Information

Seems like it could be related to #31864
shell/browser/ui/inspectable_web_contents.cc
auto* browser_context = web_contents_->GetBrowserContext();
  const extensions::ExtensionRegistry* registry =
      extensions::ExtensionRegistry::Get(browser_context);
  if (!registry)
    return;
  base::ListValue results;
  for (auto& extension : registry->enabled_extensions()) {
    auto devtools_page_url =
        extensions::chrome_manifest_urls::GetDevToolsPage(extension.get());
    if (devtools_page_url.is_empty())
      continue;