### 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.h
void ShowItemInFolder(const std::string& file_system_path) override;
  void SaveToFile(const std::string& url,
                  const std::string& content,
                  bool save_as) override;
  void AppendToFile(const std::string& url,
                    const std::string& content) override;
  void RequestFileSystems() override;
  void AddFileSystem(const std::string& type) override;
  void RemoveFileSystem(const std::string& file_system_path) override;
  void UpgradeDraggedFileSystemPermissions(
      const std::string& file_system_url) override;
  void IndexPath(int index_request_id,
                 const std::string& file_system_path,
                 const std::string& excluded_folders) override;
  void StopIndexing(int index_request_id) override;
  void SearchInPath(int search_request_id,
                    const std::string& file_system_path,
                    const std::string& query) override;
  void SetWhitelistedShortcuts(const std::string& message) override;
  void SetEyeDropperActive(bool active) override;
  void ShowCertificateViewer(const std::string& cert_chain) override;
  void ZoomIn() override;
  void ZoomOut() override;
  void ResetZoom() override;
  void SetDevicesDiscoveryConfig(
      bool discover_usb_devices,
      bool port_forwarding_enabled,
      const std::string& port_forwarding_config,
      bool network_discovery_enabled,
      const std::string& network_discovery_config) override;