It’s used all the time in the freshwater aquarium hobby, which still kinda blows my mind. I use it to attach certain species of live plants to rock and driftwood

As in, it will keep holding if exposed to water after it has set, not "you can apply it under water", correct?

The water will cause it to cure very quickly, so it will be hard to establish a good bond. Normally it cures because of the presence of water in the air.

It forms a skin almost immediately but if you squish the bubble between two objects it will pop and you can do full underwater gluing.

But can it attach underwater, with all the water between the two surfaces?

No. Maybe you could make it work but I wouldn’t count on it. Marine epoxy is designed for this task, it can be applied and attached fully submerged with no issues.

Turns out people with more experience than I have in using superglue underwater say it does work, I was wrong!

yes this is how corals are propagated

I mean you can apply it under water and it works just fine. I use it all of the time in my aquarium.