I wonder if comparing to Lichess might be apples and oranges.
In chess, the very term “problem” implies uniqueness of the solution. IOW, a “problem” with multiple different ways to reach the goal (sometimes allowing for things like forced repetition) is not a problem. While already the existence of a “Best Move” category for go problems seems to imply there are other kinds (and I can confirm this from personal experience, and sometimes disappointment, being a sort of refugee from chess).
As a variation of things tsumego sites do (loosely on topic of the OP), goproblems https://www.goproblems.com added a puzzle rush feature where you get three lives and a limited amount of time to solve as many puzzles of increasing difficulty as you can.
And of course goproblems was the example given at the start of the thread for using Elo for puzzles.
One could relax the requirement of a single unique solution. And you can also let users rate puzzles as “good” or “bad”, which can help filter out weird incomprehensible AI stuff