If Water Walk has been cast on someone, can they still choose to submerge themselves or is their buoyancy now determined and final until the spell ends?
RAW is Insufficiently Explicit
Water Walk says...
This spell grants the ability to move across any liquid surface [...] as if it were harmless solid ground.
Spells in D&D tend to do only what they say on the tin. At first blush, this one is pretty clear. However, they're also meant to be parsed with normal human language. Having the ability to do something does not explicitly require one to do that thing.
However, it also says...
If you target a creature submerged in a liquid, the spell carries the target to the surface of the liquid at a rate of 60 feet per round.
This part of the spell doesn't use language that introduces the possibility of caveats - if the subject is submerged, they rise. There is no indication it ends after they surface.
With the first part being theoretically optional, but the second part clearly mandatory, there are two choices.
Treat the 60 feet as negative downward movement. A sufficiently fast character (able to Swim more than 60 feet in a turn) could choose to dive into the surface, but wouldn't get very far. A slower character couldn't even try to swim down.
Apply the 60 feet upward at the end of each character's turn - a character who could swim 30 would get down 30 feet, then be pushed back to the surface at the end of their turn.
Personally, I've ruled the second without complaint from players, but the first is an equally reasonable approach.
Yes you can voluntarily go underwater
This spell grants the ability to move across any liquid surface (PHB 287)
Having an ability does not force you to use it every time when applicable. If they wished for it to be otherwise, they could have worded it differently, like "Creatures affected by the spell do not sink in liquids, but can walk on their surface.".
What might be a source of confusion is that:
If you target a creature submerged in a liquid, the spell carries the target to the surface of the liquid
This applies only when you target a creature submerged in a liquid, i.e. at the time of casting. The creature cannot "opt out" of it, though. The spell explicitly forces it up at the stated rate.