### 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
if (embedder_message_dispatcher_) {
    if (managed_devtools_web_contents_)
      view_->ShowDevTools(activate);
    return;
  }
  activate_ = activate;
  
  
  embedder_message_dispatcher_ =
      DevToolsEmbedderMessageDispatcher::CreateForDevToolsFrontend(this);
  if (!external_devtools_web_contents_) {  
    managed_devtools_web_contents_ = content::WebContents::Create(
        content::WebContents::CreateParams(web_contents_->GetBrowserContext()));
    managed_devtools_web_contents_->SetDelegate(this);
    v8::Isolate* isolate = v8::Isolate::GetCurrent();
    v8::HandleScope scope(isolate);
    api::WebContents::FromOrCreate(isolate,
                                   managed_devtools_web_contents_.get());
  }
  Observe(GetDevToolsWebContents());
  AttachTo(content::DevToolsAgentHost::GetOrCreateFor(web_contents_.get()));
  GetDevToolsWebContents()->GetController().LoadURL(
      GetDevToolsURL(can_dock_), content::Referrer(),
      ui::PAGE_TRANSITION_AUTO_TOPLEVEL, std::string());
}
void InspectableWebContents::CloseDevTools() {