Why does my cat only drink water right after eating?

This is one of the most normal drinking patterns there is, especially on dry food. Kibble has very little moisture, so a cat’s body prompts thirst shortly after a meal to help process it, the same way a salty snack makes a person reach for water afterward. If she is drinking at other points in the day too, or drinking a reasonable amount overall, this is nothing to change. It only becomes worth a closer look if she stops drinking at other times altogether or the after-meal drinking becomes noticeably heavier over a few weeks.