Will there eventually be a "xcloud app" on the xbox itself? To stream games instead of...

No, the Streaming app for xCloud allows for online play of those xCloud games or will allow you to stream your Xbox games to your phone.

the xbox is actually on when streaming, impossible to be off when streaming as it does all the work, are you sure your not streaming a game from xcloud instead as that does not use your console.

They need to make a unified app, with Game Pass, Console Streaming/xCloud, Xbox App and Rewards

The games will probably be able to be played using the Xbox cloud service XCloud that is coming soon. You won't be able to download the game, but stream it instead.

I am accepted in the game stream preview, but I was not streaming at the time of using the game pass mobile app. Its the game pass app itself that is lagging. I even logeed out of everything except the game pass mobile app on google play store. I had all
xbox apps on my phone uninstalled as well, except the game pass mobile app. I am a part of Project XCloud if thats what you're asking.