So I’ve explored this a little bit more and, unfortunately, it isn’t an easy addition as it stands.
Here is why: Trello’s web client keeps a local cache of data it needs to render Trello boards. When you first load a board, it asks the API for all of the cards on the board and all of the things it needs to render a board-level view. It stores that data in its local cache and uses it as needed. The majority of what is available in the client library for Power-Ups is being pulled from what is in that cache. However, the cache doesn’t get the checklists for a card until it needs them - when you’re looking at a card back. So we could give you incomplete data - just pass along what we already know about in the cache. Or we could make a new request to the API asking for the checklists. This gets into a place where we need to understand the impact of making a new request for data on your Power-Up’s behalf and the impact it could have on the load performance of a board.
We don’t have a solid answer on how we’d want to implement this yet, but it isn’t something we’ve said we will never do. Our team will keep it in the backlog, but right now it isn’t something that is highly prioritized.
Our recommendation at this time is that you should use the REST API to get checklists.