Here's my solution: get (or be) a strong tech lead that can write tickets, negotiate features, and steer technical direction. They can optionally run the team as well, or that can have a separate person, who is still technical, in the team who keeps the trains running on time with meetings etc. The product person is slightly more distant; not in every meeting, and the tech lead makes sure work is synced with the product requirements, which are documented not in tickets, but at a higher level in written+diagram form.

That way you don't have "product" people who are really just status reporting for the team, or "product" people who are really just writing bad tickets that need rewriting. You have actual product people who focus on where the product should be going.

You also don't have a "delivery manager" role. The team needs to be steered into doing this by a decent lead who can do the 3% admin required to keep on top of this sort of thing.