Gmail has had the "important" flag for ages, and that's done automatically. The issue is training the AI to work for your data (e.g. I find Gmail still hasn't picked up the differences in spam I get, and so some specific spam still going to my inbox, and some specific ham ends up in spam).
Unfortunately, just because one provider provides a good AI, doesn't mean others will (and in a work context, you may be stuck with the bad one).
GPT-3 has the API available for those who want it, and it can do fine tuning, so for OP's specific use case it feels like the only limit is the size of one's wallet.
Unfortunately, just because one provider provides a good AI, doesn't mean others will (and in a work context, you may be stuck with the bad one).