If you just want to know if a player is a premium member, than a single API call is all that is needed:
- https://api.chess.com/pub/player/Eyal282 -- the "status" field says "basic" (i.e., not a premium account)
- https://api.chess.com/pub/player/whitedrake -- the "status" field says "premium"
I don't think that the published API currently offers to get the information if a given player is gold, platinum or diamond, though.
Lichess does it, searching up a player's username will return profile preferences, patron status, rating, etc... And it makes everything much easier, because all you need is one query. I have a discord bot that shows wings for Lichess patrons for not for Chess.com, because I don't want to bother 2 API calls just for the extra diamond / gold icon for premium members.