Several product managers I'm familiar with do the bare minimum. Engineers figure this out real quick and will not respect it. This is why they probably don't answer you in a timely manner. Not saying this is you, but some PMs barely understand their own products and simply forward emails between the customer and the engineering team. They are more like project managers, don't understand the details, and very little value or vision is added.

(As for the meetings, just start skipping some of them. Most meetings are useless and could be emails or a couple lines in slack.)