I'd use the same things we use for all the other things we run in the cloud, nothing special about an AI model here. Probably holds true if you think about input/output monitoring too, it's going to be called through an API, and there are plenty of tools for monitoring that as well.

Ideally your cloud provider has an easy to use solution. If not, there are monitoring services you can pay for as well. Running the open source alternatives takes some expertise.