OBS should work with WebView2 exports - last I checked it worked with some modes, but there were other modes that didn't work, so you have to get the right mode. From this post:
I can successfully capture a WebView2 export with OBS using either the display capture (suitable for a fullscreen game) or window capture with capture method Windows 10. So there do appear to be working fullscreen and windowed capture methods in OBS. If some other mode that you want to use doesn't work, it would be best to report it to OBS - it's their software and it's OBS's job to be able to capture things no matter what the app does.
The current state of overlay support (which I think might handle the screenshot feature too) is explained in the Steamworks plugin documentation. In short, we're stuck for the time being, but it's possible Valve could update Steam, or Microsoft could update WebView2, to fix it.