The twitchy multiplayer game I played the most was Destiny 2, and I didn't observe any worse lagging than on Steam with the same internet connection. I can't remember if Destiny on Stadia was cross-platform - it very well could be that all other players were on Stadia too and were equally hampered.

I didnt try stadia, but I did try a PlayStation Now trial some time ago. I only played single player games, but some were first person shooters where you’d expect lag to matter. My experience was also very good and I didn’t have any issues with lag. I kept forgetting that I was streaming.

But I have gigabit internet (and before I got that, had 300 Mb/s) and played with a wired connection, so that’s likely a contributor to my positive experience.