### 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
if (!in_memory && !partition.empty())
    path_ = path_.Append(FILE_PATH_LITERAL("Partitions"))
                .Append(base::FilePath::FromUTF8Unsafe(
                    MakePartitionName(partition)));
  BrowserContextDependencyManager::GetInstance()->MarkBrowserContextLive(this);
  
  InitPrefs();
  cookie_change_notifier_ = std::make_unique<CookieChangeNotifier>(this);
#if BUILDFLAG(ENABLE_ELECTRON_EXTENSIONS)
  if (!in_memory_) {
    BrowserContextDependencyManager::GetInstance()
        ->CreateBrowserContextServices(this);
    extension_system_ = static_cast<extensions::ElectronExtensionSystem*>(
        extensions::ExtensionSystem::Get(this));
    extension_system_->InitForRegularProfile(true );
    extension_system_->FinishInitialization();
  }
#endif
}
ElectronBrowserContext::~ElectronBrowserContext() {
  DCHECK_CURRENTLY_ON(BrowserThread::UI);
  NotifyWillBeDestroyed();
  
  BrowserContextDependencyManager::GetInstance()->DestroyBrowserContextServices(
      this);
  ShutdownStoragePartitions();
  BrowserThread::DeleteSoon(BrowserThread::IO, FROM_HERE,
                            std::move(resource_context_));
}
void ElectronBrowserContext::InitPrefs() {