LOL!
Yes, catering can mean food service.
Catering can also mean serving or accommodating a specific population. For example, a rehabilitation expert that caters to athletes.
I've not seen the word catering used frequently in reference to gifted, and when I have it has been in a negative sense of pandering. For example, a shaming or guilt-inducing statement such as "We're not here to cater to every whim of a gifted child" in response to a child needing advanced academics because they've mastered the currently prescribed curriculum years earlier.
The thread subject having the words "catering school" does invoke thoughts of
Master Chef Junior.
I agree it must be a language difference thing, possibly specific to the OP's locale?