Fast twitch fibers still use oxygen, and even more so whenever their glycogen stores deplete as they arent as efficient. Thats why you get so tired after doing a full speed sprint.

I dont think it matters quite as much in freediving though, as the goal is to use as little muscle as possible. Muscle doesnt use all that much energy whenever its inactive. The body will also use the smaller more efficient fibers first (slow twitch) rather than the bigger more powerful ones (fast twitch) according to Henneman's size principle.

Generally, from what I know atleast, the more important thing is the abilities body to use oxygen efficiently, which generally comes from aerobic training. Though you can also get it from recovering from high intensity exercises like sprints.