It seems that docker desktop for linux also use /run/host-services/ssh-auth.sock as ssh socket.
See: https://docs.docker.com/desktop/features/networking/#networking-features-for-mac-and-linux
One way to detect we're running on Docker Desktop on linux could be:
➜ test docker info --format '{{ .OperatingSystem }}'
Docker Desktop
➜ test docker info --format '{{ .OperatingSystem }}'
Ubuntu 24.04.1 LTS