### 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

16.0.0 - 16.0.5

### What operating system are you using?

Windows

### Operating System Version

Windows 7 x64 SP1

### What arch are you using?

x64

### Last Known Working Electron version

15.3.4

### Expected Behavior

Devtools should have a dark mode applied when the settings is set to 'Dark Mode'. 

### Actual Behavior

When switching to dark mode, it displays the message that 'Devtools requires a reload' but when I click on the reload button it does nothing. Restarting the app has no effect as well and stays on the light mode.

This worked fine on the previous 15.3.2 version.




### Testcase Gist URL

_No response_

### Additional Information

One thing I noticed, when updating from the last version (15.3.2) the dev tools will show up with dark mode enabled on the first run but on subsequent runs, it reverts back to light mode.
shell/browser/ui/inspectable_web_contents.cc
content::ChildProcessSecurityPolicy::GetInstance()->GrantRequestOrigin(
        web_contents_->GetMainFrame()->GetProcess()->GetID(),
        url::Origin::Create(extension->url()));
    auto extension_info = std::make_unique<base::DictionaryValue>();
    extension_info->SetString("startPage", devtools_page_url.spec());
    extension_info->SetString("name", extension->name());
    extension_info->SetBoolean(
        "exposeExperimentalAPIs",
        extension->permissions_data()->HasAPIPermission(
            extensions::mojom::APIPermissionID::kExperimental));
    results.Append(std::move(extension_info));
  }
  CallClientFunction("DevToolsAPI.addExtensions", &results, NULL, NULL);
}
#endif
void InspectableWebContents::SetInspectedPageBounds(const gfx::Rect& rect) {
  DevToolsContentsResizingStrategy strategy(rect);
  if (contents_resizing_strategy_.Equals(strategy))
    return;
  contents_resizing_strategy_.CopyFrom(strategy);
  if (managed_devtools_web_contents_)
    view_->SetContentsResizingStrategy(contents_resizing_strategy_);
}
void InspectableWebContents::InspectElementCompleted() {}
void InspectableWebContents::InspectedURLChanged(const std::string& url) {
  if (managed_devtools_web_contents_)
    view_->SetTitle(
        base::UTF8ToUTF16(base::StringPrintf(kTitleFormat, url.c_str())));
}
void InspectableWebContents::LoadNetworkResource(DispatchCallback callback,