I haven't deeply researched the finance, but bottom of https://www.gnome.org/ says Hosted by Red Hat, and Red Hat's logo is on the carousel of GNOME supporters. Meanwhile on the end of https://kde.org/ home page there's a list of patrons which have SUSE and Canonical but not Red Hat.
Yup, but you'll also find e.g. Fedora on lists like https://akademy.kde.org/2022/sponsors/ (and Red Hat was on there not so long ago too, iirc) so it's not completely out of the blue that the communities are involved with each other :-)
