Your goal here would be to make it easier for them to search than to ask.

Have a generic link in which they could find most of their answers. When they ask something that's in the docs, reply with a link. When they ask something that's not, add it to the docs, and reply the answer + "that was missing - I've just added it to the docs" to reinforce the fact that this time it was OK to ask and that they helped you improve the docs.

The more someone asks you things that were searchable, the more you delay the answer with the link. If you make it quicker to search than to ask, that'll encourage them to search.

If they still don't change the attitude, let your manager work. If that doesn't bring any other change - it may be time to move to another team/manager.