API endpoints for this stuff actually do exist, just not documented :) For example, to get user's info, perform simple GET request:
For user_id=1 the result is:
You can find other APIs in the itch client's code https://github.com/itchio/itch/blob/master/src/api/index.ts . Obviously no guarantee that it will work in future. Would be very nice if these APIs were officially supported and documented.