Valve has truly headless runner (gamescope) for Linux, e.g. you can start it manually from command-line over ssh

  gamescope \
    --backend headless \
    -W 1920 -H 1080 \
    -w 3840 -h 2160 \
    -r 60 \
    --cursor-scale-height 1080 \
    --force-grab-cursor \
    -- steam -gamepadui -pipewire-dmabuf

You still need the initial setup for pairing.

But it has many issues compared to Games on Whales, for example, which is much more efficient and scales cursor better.

https://github.com/ValveSoftware/gamescope