Hey @Golld and @samuxip Welcome to the UX Mastery community!
There isn’t a straight-forward answer to what deliverables you (or the team) will create for a project – that would depend many factors such as the scale of the re-design, the resources you have available, budget and time constraints.
PMs can create the user stories – assuming you’re working in an agile team – but those would be created before the design and research activities. User stories should be written as problem statements that the entire team (designers, researchers, designers and other stakeholders) tackle together.
If you’ve already fleshed out the design and only need to hand it over to the devs for implementation (aka waterfall), the user stories wouldn’t serve any purpose.
I would suggest that if you’re undertaking a re-design, you should still create the user stories – after all your re-design should solve a problem. If the re-deisgn doesn’t improve on the existing designs, then the effort would be purely cosmetic