I was trying to verify if this was karaoke related because if it's not there might be better places to ask this question.

This is an interesting request. You would think there would be a simple cheap device to accomplish this but I couldn't find any.

But looking around you might be able to use the Cast feature of the Chrome browser to cast the screen.

Maybe a cheap Chromebook like this one?

https://smile.amazon.com/Lenovo-Chromebook-Processor-Graphics-82BA0003US/dp/B087YW8FQB

It should have everything needed including the mic input to connect to the mixer. You would just need an adapter to break out the mic input and headphone output.