Having looked more into it, I’m positive. Consumers of the public API are not bound by the licensing terms in the same way as someone serving the API is.
Here’s one of the many references for that: Does accessing the REST interface of a AGPL-licensed server make the client a derivative work? - Open Source Stack Exchange
(edit) Another one: If I use a public API endpoint that has its source code licensed under AGPL in my app, do I need to disclose my source? - Open Source Stack Exchange