Merge Twitch and YouTube?

Both make live streams, so why can you do it on YT in such a way that you transfer the screen from https://www.twitch.tv/...twitch.tv/ to https://www.youtube.com/...utube.com/ in order to be able to watch. Or simply "combine" both

What you mean is dual streaming.
That means streaming on 2 sources at the same time, in your case Youtube & Twitch.

You can do that via external sites like http://restream.io.

But that is not seen with pleasure & is even prohibited from affiliate status anyway.