The monk class feature Unarmored Movement says:
At 9th level, you gain the ability to move along vertical surfaces and across liquids on your turn without falling during the move.
I am looking for an answer based in the rules as written, although interpretations and opinions are welcome.
I assert the rules support a notion of turns as meta-constructs useful for examining the game world at intervals, as opposed to a game world law of nature. As an example, if a character jumps and "runs out" of jump at the end of their turn while still jumping, I view the character as ending their round in mid-air, and that the jump gets continued on the character's next turn. I don't actually have rules citations to support my assertion, unfortunately.
This is important because I think it affects how far the monk can move along vertical or liquid surfaces. I don't know how, though.
As an example, let's assume a monk with 30' movement is 10' away from a 30' wide body of water. The monk moves 10' on land and then 20' on water and then the monk's turn is over. Does the monk fall in the water?
A slightly different example. Let's assume the monk has 30' of movement and is at the edge of a 1000' wide body of water. How far can the monk move before falling in?
One answer might be the monk can move its movement, then it is no longer able to stay above the water and gets dunked. If this is the case, can the monk get back up on the water and keep moving?
One perhaps unintuitive answer is that there is actually no limit on how far the monk can move without falling, which means the monk could move across liquid until the monk needs to stop for some reason, say exhaustion, then they fall in.
Not to be absurd, but in this case, I think the monk could "ice" skate on the water, and do swirls and tricks and stuff. Okay, yes, that's actually absurd.
To summarize: how far can a 9th level monk move along a vertical surfaces and across liquids without falling?
to the end of the monk's turn, then the monk needs to be on solid ground or fall
the monk's movement distance, even if that leaves the monk suspended on the vertical surface or the liquid between turns
as far as the monk wants, as long as the monk keeps moving