### Preflight Checklist

- [X] I have read the [Contributing Guidelines](https://github.com/electron/electron/blob/master/CONTRIBUTING.md) for this project.
- [X] I agree to follow the [Code of Conduct](https://github.com/electron/electron/blob/master/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 feature request that matches the one I want to file, without success.

### Electron Version

13.1.7

### What operating system are you using?

Windows

### Operating System Version

Windows 10 version 20H2

### What arch are you using?

x64

### Last Known Working Electron version

12.0.15

### Expected Behavior

Checking `navigator.userAgentData` in Chrome 91 returns an array of brands appropriately. Electron 13/14 do not return anything.

This appears to then become a problem for my situation. I am posting a form with hidden variables to a third-party vendor I work with. This form post ultimately loads an iframe.

Expected: As it does in Chrome 91, load the iframe from this third-party vendor.

### Actual Behavior

A header of "sec-ch-ua" is included in the request to the third-party vendor and it is blank. They are rejecting the post because of an invalid header. I suspect this is because Chrome 13/14 does not make this hint data made available correctly.

I tried loading various sites in Chrome 91 that do load brand names in Electron 13/14 and they are empty if you review `navigator.userAgentData`.

### Testcase Gist URL

_No response_

### Additional Information

_No response_
shell/browser/electron_browser_context.cc
auto prefs_path = GetPath().Append(FILE_PATH_LITERAL("Preferences"));
  base::ThreadRestrictions::ScopedAllowIO allow_io;
  PrefServiceFactory prefs_factory;
  scoped_refptr<JsonPrefStore> pref_store =
      base::MakeRefCounted<JsonPrefStore>(prefs_path);
  pref_store->ReadPrefs();  
  prefs_factory.set_user_prefs(pref_store);
#if BUILDFLAG(ENABLE_ELECTRON_EXTENSIONS)
  if (!in_memory_) {
    auto* ext_pref_store = new ExtensionPrefStore(
        ExtensionPrefValueMapFactory::GetForBrowserContext(this),
        IsOffTheRecord());
    prefs_factory.set_extension_prefs(ext_pref_store);
  }
#endif
#if BUILDFLAG(ENABLE_ELECTRON_EXTENSIONS) || \
    BUILDFLAG(ENABLE_BUILTIN_SPELLCHECKER)
  auto registry = base::MakeRefCounted<user_prefs::PrefRegistrySyncable>();
#else
  auto registry = base::MakeRefCounted<PrefRegistrySimple>();
#endif
  registry->RegisterFilePathPref(prefs::kSelectFileLastDirectory,
                                 base::FilePath());
  base::FilePath download_dir;
  base::PathService::Get(chrome::DIR_DEFAULT_DOWNLOADS, &download_dir);
  registry->RegisterFilePathPref(prefs::kDownloadDefaultDirectory,
                                 download_dir);
  registry->RegisterDictionaryPref(prefs::kDevToolsFileSystemPaths);
  InspectableWebContents::RegisterPrefs(registry.get());
  MediaDeviceIDSalt::RegisterPrefs(registry.get());