I dont mean to be too pedantic but open source for a linux desktop environment kinda should go without saying?
Rather, I couldn't imagine using a closed source one.
They exist, for example SteamOS has closed source desktop shell based on Steam client
Their gamescope compositor is free software at least.
Good point, available at https://github.com/ValveSoftware/gamescope BSD license
Was it Caldera that shipped a linux with Motif?
(We're talking three decades ago now)
fwiw I can remember all the turmoil when Qt had no free tier and KDE was work of the devil
If you or anyone else want a trip down memory lane around that topic, peppered with some interesting revelations, this video is worth checking out:
KDE: The Documentary — The Story of Free Software Underdogs