you could help it along by providing clues about the domain in the prompt. including what various proper nouns might indicate (assuming they're not chosen completely at random, and encode at least some meaning).

and you might find the scores it gives back about its confidence are useful for escalating to a more expensive classifier.

but also, there's no requirement to use it as a zero-shot classifier, you can provide it as many examples as you like, and prioritise giving it examples it had previously gotten wrong. and with input caching it might be economical.

I'd be surprised if they or others don't start offering a fine tuning API for models like this, like openai does for some models (or used to, I haven't checked in a long time).