### 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 feature request that matches the one I want to file, without success.

### Electron Version

16.0.2

### What operating system are you using?

macOS

### Operating System Version

macOS Monterrey 12.0.1

### What arch are you using?

arm64 (including Apple Silicon)

### Last Known Working Electron version

13

_No response_

### Expected Behavior

This configuration should produce a vibrant window:

```ts
new BrowserWindow({
    width: 800,
    height: 600,
    backgroundColor: undefined,
    vibrancy: "sidebar",
    titleBarStyle: "hidden",
    webPreferences: {
      preload: path.join(__dirname, 'preload.js')
    }
  })
```

### Actual Behavior

The window has a white background.

As of Electron 16.x vibrancy works if `backgroundColor` is not set at all, but not if it's explicitly set to `undefined`. As a consequence, if the background color is set to any value, it's impossible to unset it later.

### Testcase Gist URL

_No response_

### Additional Information

What's interesting is that this option check returns `true` if the background color is explicitly set to `undefined`:

https://github.com/electron/electron/blob/bd10b19b0cdc46cdbadb570af89305e64541b679/shell/browser/api/electron_api_browser_window.cc#L50

But this one returns `false`:

https://github.com/electron/electron/blob/bd10b19b0cdc46cdbadb570af89305e64541b679/shell/browser/native_window.cc#L208

shell/browser/api/electron_api_browser_window.cc
content::RenderViewHost* new_host) {
  if (old_host)
    old_host->GetWidget()->RemoveInputEventObserver(this);
  if (new_host)
    new_host->GetWidget()->AddInputEventObserver(this);
}
void BrowserWindow::RenderFrameCreated(
    content::RenderFrameHost* render_frame_host) {
  if (!window()->transparent())
    return;
  content::RenderWidgetHostImpl* impl = content::RenderWidgetHostImpl::FromID(
      render_frame_host->GetProcess()->GetID(),
      render_frame_host->GetRoutingID());
  if (impl)
    impl->owner_delegate()->SetBackgroundOpaque(false);
}
void BrowserWindow::DidFirstVisuallyNonEmptyPaint() {
  if (window()->IsClosed() || window()->IsVisible())
    return;
  
  
  auto* const view = web_contents()->GetRenderWidgetHostView();
  view->Show();
  view->SetSize(window()->GetContentSize());
}
void BrowserWindow::BeforeUnloadDialogCancelled() {