Have you looked into Moonlight? Nvidia is sunsetting GeForce Experience which would be a convenient streaming server, but Sunshine seems to be almost on par now, latency wise. So you‘d run Sunshine on your host machine, and Moonlight on the Steam Deck. I’ve seen people report a minimal input lag of just 1 frame @ 4k60 (with most recent Sunshine versions, there was a big leap recently) but haven’t tried it myself yet.
One big upside of Sunshine is that you can log into your host user remotely. So you could wake up the host with WoL and do the rest on the Deck.