For the most part, it depends on what you'd call "official".
afaik, SRB2Kart is developed by a team outside of Sonic Team Jr known as Kart Krew, as you may already know. Although this automatically makes it unofficial, the SRB2 Message Board does still have direct integration for it. (i.e. it gets its own section in Addons & More), and is otherwise completely endorsed by Sonic Team Jr.
On a more technical note, the EXE used to run SRB2Kart is actually based on SRB2 2.1, and it's not even all that different. However, the dependency files for the two games are completely different.
So, it's sort of neither, and sort of both, at the same time.