Just wondering if anyone has been streaming games from their desktop and how it works when they put their Deck to sleep.

I am thinking about building a new desktop, but I almost exclusively play on my Deck and so it would primarily be for streaming to the Deck. My main concern is that the game will continue to run on the desktop either using a lot of electricity or causing me to die in game. I play several Souls-like games that don't allow you to pause and will often have to break away to do something else at a moment's notice.

Anyone have any recommendations for a game that's like Dance Dance Revolution? My wife really liked that game back in the day and I am looking to get her it or something like it as a gift.

We have a PS5 and Xbox One S. We also have a Switch that I could get a dock hooked up to the TV, but she usually uses it in handheld mode. If there's not really any options for those systems we also have some older systems in storage while we finish some construction that I could dig out (most systems dating back to SNES).