It sounds like the product people are sitting in long meetings. Have you considered the idea that people were already disengaged in those meetings, they were just putting up a better front because they could tell everyone was watching them closely in person?

And now that they are at home, they are not trying as hard to pretend they are listening closely, and since they are more comfortable, they are staying in the meetings and saying what they want? Whereas before they would let the most assertive person talk, and after a few minutes could not tolerate the in person meeting anymore and so pretended that they were all in agreement so you would let them go, knowing they would work out the actual details amongst themselves later?

And now they don't have the option of working things out after the meeting, which is another reason the meetings are taking longer.

The biggest issue for you is probably that you have a lot of wasted time where only a part of the team is working together in the meeting but other people who are not involved in that part are just waiting for them to finish.

Do some research on the tools that engineers use to work asynchronously and train your product team. Also consider smaller video chat meetings, and chat rooms, etc.