### 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::DevToolsAgentHost* agent_host) {}
void InspectableWebContents::RenderFrameHostChanged(
    content::RenderFrameHost* old_host,
    content::RenderFrameHost* new_host) {
  if (new_host->GetParent())
    return;
  frontend_host_ = content::DevToolsFrontendHost::Create(
      new_host, base::BindRepeating(
                    &InspectableWebContents::HandleMessageFromDevToolsFrontend,
                    weak_factory_.GetWeakPtr()));
}
void InspectableWebContents::WebContentsDestroyed() {
  if (managed_devtools_web_contents_)
    managed_devtools_web_contents_->SetDelegate(nullptr);
  frontend_loaded_ = false;
  external_devtools_web_contents_ = nullptr;
  Observe(nullptr);
  Detach();
  embedder_message_dispatcher_.reset();
  if (view_ && view_->GetDelegate())
    view_->GetDelegate()->DevToolsClosed();
}
bool InspectableWebContents::HandleKeyboardEvent(