Obviously not every item in the backlog has a full design, for work that might be years out.
But yes, the next few items for the team to work on should always have the necessary specifications to start work. Whether it's UX mocks or a requirements document or whatever. Having that stuff ready to go is a primary job of the PM who manages the backlog.
Obviously the engineering team then has to break it down further into tasks to complete, but that's what engineering is. And you will run into areas that turned out to be underspecified and the PM needs to liaison with other folks to figure out answers, but again that's part and parcel. That's not generally stopping the whole team from work, and teams often work on multiple features at once so even being temporarily blocked on one doesn't keep you from progress on another.