Somehow, given it was his idea to move the character in this direction (and his obvious interest in Superman motifs, e.g. Brightburn), I always assumed he would be directing.
Yeah, such as Comet, who isn’t even her horse - or a horse at all - but a cursed centaur who’s in love with her. (No, really. Yeah, it’s perverse.)
Weirdly, Superman’s dog and monkey (Krypto and Beppo) are Kryptonian super-animals, but Supergirl’s are not (Streaky the Supercat is an Earth cat altered by some kind of kryptonite). Which is kind of weird, really.