dnd 5e – Does a bronze dragon’s wing attack work underwater?

An adult bronze dragon has a lair deep inside of a coastal mountain. To get to where she hides her stuff (and where she is keeping a clutch of eggs warm) an adventuring party needs to swim deep underwater, then through a water-filled passageway, and then up to emerge on the surface of a lake inside of the mountain (they end up inside a very large dome, roughly).

If the dragon detects them before they surface, and leaps into the water (she has a swimming speed of 40) can she successully use her wing attack (a Legendary Action) against the party while fighting underwater?

The dragon beats its wings. Each creature within 10 feet of the dragon must succeed on a DC 20 Dexterity saving throw or take 14 (2d6 + 7) bludgeoning damage and be knocked prone. The dragon can then fly up to half its flying speed.

My instinct is that she cannot use the wing attack, and I don’t think that she can “fly” in the water (for half of her flying speed) by beating her wings. Whether or not dragons swim by using their wings, or if they move more like a sea serpent, is unclear but I tend to believe the latter.

Underwater Combat rules leave me little to work with. The restrictions are

When making a melee weapon attack, a creature that doesn’t have a swimming speed (either natural or granted by magic) has disadvantage on the attack roll unless the weapon is a dagger, javelin, shortsword,
spear, or trident. A ranged weapon attack automatically misses a target beyond the weapon’s normal range. Even against a target within normal range, the attack roll has disadvantage unless the weapon is a crossbow, a net, or a weapon that is thrown like a javelin (including a spear, trident, or dart). Creatures and objects that are fully immersed in water have resistance to fire damage. (Basic Rules, Ch 9, p. 80)

She has a swimming speed, so her tail attack or her bite attack are not at disadvantage. Her Wing attack doesn’t seem to be either of those two attack categories since it requires a Dexterity saving throw and there is no “to hit” roll.

Does the dragon retain her ability to use that legendary action, Wing Attack, if she is fighting underwater?

This also becomes an issue if they steal some stuff, or an egg, and she pursues them. Can she knock them prone with a wing attack during the pursuit? Answering the general question takes care of that specific case.
(While I am also puzzling over ‘prone’ while swimming underwater, I don’t need that answered for the purposes of this question and @Medix2 kindly linked to a realted question)