I just recently got google stadia on my phone and laptop and I have major issues. The mobile version doesn't read my inputs (or something like that). The games don't respond to the on-screen buttons i register and I am always stuck on the home screen of every game. For pc, the game run just darn near perfect but the moment I move the cursor every thing becomes choppy as hell, I cant say it is exactly latency from my side because the keyboard works so smoothly but the mouse just messes everything up and all games become unplayable asides from trail xrtreme that doesnt need the cursor for anything. I was really considering subscribing for stadia but God knows I wont with all the bugs on there.
Are you using experimental mode on the Stadia app?
On your laptop are you using an ethernet connection?
Which game are you trying to play?
What is your internet speed?
We need a lot more information to properly help you out.