Honestly non at all. I even took a video once with my phone of my steam deck screen next to the pc monitor and the frames were perfectly in sync. The input feels native and i have zero latency with that. I remember years ago it indeed wasn’t that good. But nowadays its so perfect!

I even play competitive counter strike that way.

The stats show around 1ms. And that is network and decoding combined.

As long as you are at home, its indistinguishable from directly plugging in a mouse+keyboard and monitor.