### 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
content::WebContents* source,
    const content::NativeWebKeyboardEvent& event) {
  auto* delegate = web_contents_->GetDelegate();
  return !delegate || delegate->HandleKeyboardEvent(source, event);
}
void InspectableWebContents::CloseContents(content::WebContents* source) {
  
  CloseDevTools();
}
void InspectableWebContents::RunFileChooser(
    content::RenderFrameHost* render_frame_host,
    scoped_refptr<content::FileSelectListener> listener,
    const blink::mojom::FileChooserParams& params) {
  auto* delegate = web_contents_->GetDelegate();
  if (delegate)
    delegate->RunFileChooser(render_frame_host, std::move(listener), params);
}
void InspectableWebContents::EnumerateDirectory(
    content::WebContents* source,
    scoped_refptr<content::FileSelectListener> listener,
    const base::FilePath& path) {
  auto* delegate = web_contents_->GetDelegate();
  if (delegate)
    delegate->EnumerateDirectory(source, std::move(listener), path);
}
void InspectableWebContents::OnWebContentsFocused(