The practical answer for right now is that I don't want software screen capture, but it also does not do any of the things I wanted to be able to do by having remote inputs directed to the hardware rather than simulated in software. Namely it requires software installation on the server, which means OS support becomes a thing, you can't use it in BIOS/firmware, etc.
Sunshine works on linux and windows, screen capture uses parts of the gpu meant to do that as result you get lower latency than separate capture and encode.
If you're like playing Apex/Valorant/PUBG/Dota and such, and scared that use of remote plays might get flagged, you could just use HDMI-in MPEGTS-out Ethernet capture streamer building scale HDMI extender thing(I don't know the actual categorical name). Inputs can be handled by a separate device, or just wireless keyboard/mouse.
Note that if anti-cheat is a concern, common dev boards like Arduino Leonardo and Pi Pico could also trigger flagging, so maybe that needs to be done slightly differently too(assuming the intent is good and this don't count towards anti-cheat evading in whatever you're doing).