RAW is unclear, but I believe the intent is that you are still limited to a certain distance; it's not indefinite
RAW, the feature is worded in a way that only makes sense in combat when time is divided up into turns, therefore it is unclear what this means outside of combat. However, if I guess the intent of the feature, then I believe it is equivalent to saying:
... you gain the ability to move along vertical surfaces and across liquids as far as your movement will allow1 without falling.
Therefore, the way I would rule it is that the amount of liquid surface you can run across (or how far up a wall you can run) before you fall would match your maximum movement (meaning your current speed plus however much additional movement you can achieve from Dashing).
If it was intended to let you run across an ocean or all the way to the top of a giant tower, then why would the feature have you fall at the end of your turn during combat, rather than just having you stay where you are on a liquid or vertical surface between turns? From this, we can deduce that the feature is not intended to allow indefinite movement across liquids or vertical surfaces.
Also note that, since we're out of combat and therefore not dividing time and movement in turns, we can assume that you start your sprint across water or up a wall at the edge of the water or at the bottom of the wall, whereas in combat you might have to move up to the edge of the water or the wall first (also, you might not have an action/bonus action to spend to Dash, whereas outside of combat this can be assumed more easily); that's why I would assume your maximum movement outside of combat (if I were your DM).
1. What I mean by this is your current speed, including how much your movement can be increased via Dashing, such that this matches the maximum amount of movement you could achieve within a turn during combat. I hope this is clear enough from this wording.