Large scale usability tests are pretty rare for open source software. Gnome is one of the few exceptions having some testing paid for by Sun Microsystems for Gnome 1 and then again by Novell for Gnome 2 around 2005.

From this they developed the Gnome HIG (human interface guidelines), which was used extensively in Gnome 2 and formed the basis for much of what they wanted to accomplish in Gnome 3.

Since the Novell test they had some ad-hoc usability testing, but nothing large or ran by professional usability testers.

Example:

https://renatagegaj.wordpress.com/2016/08/23/gnome-usability...