### 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
pref_service_->SetBoolean(kDevToolsSyncPreferences,
                            kSyncDevToolsPreferencesDefault);
  DictionaryPrefUpdate unsynced_update(pref_service_, kDevToolsPreferences);
  unsynced_update.Get()->DictClear();
  DictionaryPrefUpdate sync_enabled_update(
      pref_service_, kDevToolsSyncedPreferencesSyncEnabled);
  sync_enabled_update.Get()->DictClear();
  DictionaryPrefUpdate sync_disabled_update(
      pref_service_, kDevToolsSyncedPreferencesSyncDisabled);
  sync_disabled_update.Get()->DictClear();
}
void InspectableWebContents::GetSyncInformation(DispatchCallback callback) {
  
  base::Value result(base::Value::Type::DICTIONARY);
  result.SetBoolKey("isSyncActive", false);
  std::move(callback).Run(&result);
}
void InspectableWebContents::ConnectionReady() {}
void InspectableWebContents::RegisterExtensionsAPI(const std::string& origin,
                                                   const std::string& script) {
  extensions_api_[origin + "/"] = script;
}
void InspectableWebContents::HandleMessageFromDevToolsFrontend(