The baby is used to falling asleep with his mouth full of breast milk.…

The baby is used to falling asleep with his mouth full of breast milk. We're on a mixed diet (not feeding from the breast because there's little milk, so I supplement with formula). If we give him the breast, he sucks and falls asleep. If we give him formula from a bottle, he drinks it quickly and doesn't fall asleep, so we still have to feed him breast even if it's empty, only then can we sleep. How to stop falling asleep with the breast? It may spend an hour on it without getting anything from it.