### 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 SetDevicesUpdatesEnabled(bool enabled) override;
  void PerformActionOnRemotePage(const std::string& page_id,
                                 const std::string& action) override;
  void OpenRemotePage(const std::string& browser_id,
                      const std::string& url) override;
  void OpenNodeFrontend() override;
  void DispatchProtocolMessageFromDevToolsFrontend(
      const std::string& message) override;
  void SendJsonRequest(DispatchCallback callback,
                       const std::string& browser_id,
                       const std::string& url) override;
  void RegisterPreference(const std::string& name,
                          const RegisterOptions& options) override;
  void GetPreferences(DispatchCallback callback) override;
  void GetPreference(DispatchCallback callback,
                     const std::string& name) override;
  void SetPreference(const std::string& name,
                     const std::string& value) override;
  void RemovePreference(const std::string& name) override;
  void ClearPreferences() override;
  void GetSyncInformation(DispatchCallback callback) override;
  void ConnectionReady() override;
  void RegisterExtensionsAPI(const std::string& origin,
                             const std::string& script) override;
  void Reattach(DispatchCallback callback) override;
  void RecordEnumeratedHistogram(const std::string& name,
                                 int sample,
                                 int boundary_value) override {}
  void ReadyForTest() override {}
  void SetOpenNewWindowForPopups(bool value) override {}