I agree it can have one of both meanings. It goes with context:
Conditions that can cause this are poor water quality, lack of air, poor nutrition and loud noises. The goldfish is sensitive not only to his own aquatic world but to the world around his own. While it's true that goldfish can tolerate algae and muck to a certain degree, they will go into partial hibernation if their water becomes too cold. While it's unlikely that such conditions would occur in a bowl, the fish would react by sitting still at the bottom. Nitrates in the water stress the fish and make him sick; in a small bowl they build up quickly, causing disease.Sleeping is the only healthy circumstance for goldfish to hang out on the bottom of a bowl. When goldfish sleep, they simply hang somewhere, without moving much.
In such case, I think "still" (an adjective, the quality or state of being stationary - not moving or making a sound). Would be the same as "hang out" (spend time here) at the bottom of the bowl [to the fish example of before].
Taken in some contexts, yes, it may have the meaning of "continuing to happen or continuing to be done" (an adverb).
As one sentence - "The fish was still in the water." - would be indisputable that the first thought would be of continuing to happen, the word as an adjective could even occur, but it would be way less often.