I suppose it is doable?
The biggest issue you are going to face with trying to do something like this is getting the website. Godot has no support for HTML and CSS, nor does Godot support JavaScript (at least, by default). This means it would be almost impossible to actually render the HTML page in Godot.
However, I suppose what you could do instead is take a picture of the website and then use that as a texture in the background. Then you could add completely transparent buttons and other UI elements in Godot on top of the image, and simulate the workings of the website.
I think you can make Godot’s game window completely transparent and then I suppose you could position your game window over it. The huge, huge issue would be lining everything up, especially when players can have different resolutions. Another issue is you cannot send the input events through Godot to the browser, at least not that I am aware of.
So, it is probably doable, but it would be a lot of work to get it working. Honestly, it would probably just be easier to try and implement the widgets and effects you want in GDScript to get the look you want. That said, it is probably doable so long as you do not mind using C++/GDNative and spending a fair amount of time getting it all working.
Hopefully this helps :smile: