I apologize if this is an obvious question, but I could not find a similar one. I have the basic Trello package and I wonder if there is any possibility to check on which boards individual users are, without entering one by one? I know that trello enterpise has such an option, but maybe the usual one also has a similar tool?
If you mean in general, just checking a user's profile and seeing to which boards they belong to, no, that is not possible.
If you mean within a team, yes, you can see to which of your team boards a team member belongs.
This is a accessible from this menu:
This is an example on a free team:
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