Let's start by talking late, late, lategame.
The water is explicitly used as a cue for Mementos' encroachment on the real world as it transforms into the Qliphoth World. It's noticed - along with all the bone structures and other business - by both Sojiro (who due to the shot has some ambiguity as to whether he notices the pink-ish rain or the hellish architecture, but he's surrounded by the latter) and especially Mishima (who
definitely notices both, and not only reacts to the water entering under the door, but is horrified to see it's already encroached the entire train's other side when he turns around).
Now as noted, it could
just be a cue for Mementos' influence, or perhaps more specifically Yaldabaoth. But I still think there's a reason why they chose that, specifically.
The cutscenes
are however incredibly inconsistent in its portrayal, pretty much from the word go. Take the first awakening inside Kamoshida's palace:
Not a drop.
And then during the escape from Kamoshida's palace:
The characters all splash during movement - possibly a result of the same rendering engine as used for normal gameplay - but interestingly, Kamoshida's shadow doesn't seem to disturb anything. Moreover, during the actual escape there's again not a drop there.
You could theoretically argue that the sudden cleanup is a side-effect of the distortion's lessened hold on the area as the palace crumbles (as suggested by Morgana's reversion to cat form). But I'm not so sure.
In any event it seems like it both was a great visual indicator but at the same time wasn't key enough to distinguish in every cutscene and for every character, unless there's some connection or explanation I'm missing.
The only thing I'm sure of is that there's some explanation for why they chose that - the rain, the water - specifically. Maybe it's supposed to represent the contents of the Holy Grail? Best theory I can put forward without word from Atlus.
