Don't let product managers do project management
Product managers who are asked to do project management are always miserable.
Because they are performing roles that have competing needs. If they understand this then they are always fighting an existential battle over which “hat” wins.
Product managers are externally focused and make decisions based on what they learn about the market and customers.
Project managers are internally focused and make decisions based on the operational needs of the business.
These two goal are sometimes at odds with each other. One person can’t wear both hats and be effective.