I've been checking Cairo from time to time for a very long time. There was a period of active development because it was used by FireFox and, I think, had at least one dev working on it paid by Intel.
But there's no indication that the project wants your help. See https://www.cairographics.org/ and try to find the part that tells you how to submit a patch. To submit a bug you need to use a mailing list or antiquated bugzilla instance.
Cairo is ostensibly a Gnome-affiliated project as it's used in Gtk. Federico is a big deal in Gnome project.
It's telling that he had to setup up essentially a personal fork of Cairo on gitlab to do any work.
At this point in time, moving the code officially to GitHub (or GitLab) from anongit.freedesktop.org should be a no brainer if your goal is to have contributors.