In the novel Nutmeg of Consolation there's a ship that was deliberately submerged for months because it was "infected", then hauled up and refitted.
Is this a real practice and if so which ships were so treated ? It sounds like an incredible undertaking, just imagining how many men hauling on ropes even with a forest worth of blocks for mechanical advantage.
Capstans, is that it? Ratchets plus pulleys ?
While I can't speak to the popularity of the practice ( Patrick O'Brian/Richard Patrick Russ had very wide but very shallow knowledge of many things) the task of raising a wooden ship that was submerged in relatively shallow water would be rather straightforward, because any ship of the line, or of any large size, would have a bilge pump. Emptying the water out of the boat would cause it to float.
A detailed discussion of how those pumps worked can be found here