### 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
InspectableWebContentsDelegate* delegate) {
  delegate_ = delegate;
}
InspectableWebContentsDelegate* InspectableWebContents::GetDelegate() const {
  return delegate_;
}
bool InspectableWebContents::IsGuest() const {
  return is_guest_;
}
void InspectableWebContents::ReleaseWebContents() {
  web_contents_.release();
  WebContentsDestroyed();
  view_.reset();
}
void InspectableWebContents::SetDockState(const std::string& state) {
  if (state == "detach") {
    can_dock_ = false;
  } else {
    can_dock_ = true;
    dock_state_ = state;
  }
}
void InspectableWebContents::SetDevToolsWebContents(
    content::WebContents* devtools) {
  if (!managed_devtools_web_contents_)
    external_devtools_web_contents_ = devtools;
}
void InspectableWebContents::ShowDevTools(bool activate) {