The target is most likely unconscious until the end of their next turn
The feature in question states:
[...] a creature within 30 feet that looks at the prismatic beetle swarm must make a successful DC 13 Wisdom saving throw or be blinded until the end of its next turn. If the saving throw fails by 5 or more, the target is also knocked unconscious. [...]
The section on Conditions states:
[...] A condition lasts either until it is countered (the prone condition is countered by standing up, for example) or for a duration specified by the effect that imposed the condition. [...]
The problem is that this feature does not explicitly say when the unconscious condition ends, leaving us with two options:
The duration of the unconsciousness is the same as the duration of the blinded effect; that is, until the end of the target's next turn. This can be inferred from the use of also and the fact that no alternative amount of time is given.
The unconscious condition simply does not end until something that explicitly ends the unconscious condition happens (I don't know if anything explicitly does this but probably something does).
The second conclusion is, at least to me, infeasible and nonsensical. Thus I would conclude that the target remains unconscious until the end of their next turn.
Falling unconscious does not make you drop to zero hit points.
Nothing in the unconscious condition states that this occurs, and various monsters such as the Adult Brass Dragon can cause a creature to fall unconscious without their hit points lowering. Their Sleep Breath feature in particular states (emphasis mine):
[...] Each creature in that area must succeed on a DC 21 Constitution saving throw or fall unconscious for 10 minutes. [...]
Regaining hit points does not always make you conscious
The section on "Falling Unconscious" states (emphasis mine):
If damage reduces you to 0 hit points and fails to kill you, you fall unconscious. This unconsciousness ends if you regain any hit points.
The fact that gaining hit points makes you no longer unconscious is an effect unique to the unconsciousness that is specifically caused by dropping to zero hit points and does not apply to other forms of unconsciousness.