There is really no completely *safe* coating you could use since they're all (raw or liquid) plastics you harden yourself, etc, and plastics can perhaps get into foods and be eaten, especially when in contact with wet foods and hot foods. (Same for most paints.)
Hard to say if your cats would suffer from that though, especially in the beginning. Dry foods would be safer, but then you could just use your bowl as is for dry foods perhaps.
If you want to try the thickest and perhaps best clear sealer, try a regular epoxy resin**.
Or use clear polyurethane (from the hardware store) and several coats of it (the water-based type is easiest to use and will be permanent once dry).
Or you could just place a smaller glass, ceramic or metal bowl inside the bowl you made, and then there would be no real contact. And if you ever wanted to do this again, you could just cover only the *exterior* of one of those safe-material bowls with air-dry clay (or better, polymer clay--polymer clayers do that all the time, and if using a clear glass bowl/etc, any cane pattern can show through from the inside too).
Btw, if you used earthen clay ("terracotta," pottery clay, ceramic clay) rather than a different kind of air-dry clay just in a terracotta color, you could have that fired then use it but would soak up moisture (like a terracotta flower pot or the plates that can go under them), or you could apply the special glazes used for earthen clay then have it fired again to get a completely waterproof and safe food container.
** https://answersrip.com/question/index?qid=20091115185640AAXBfZF