Now before I say anything, yes I checked this discussion:
Are there official mechanics for how a climbing kit gets used in play, or is it DM discretion?
It didn't have the answer I was looking for, because it's a different question. That question is about having proficiency. Since the PHB mentions nothing about proficiency, I'm going to assume it has no associated proficiency, like using any other mundane equipment. Additionally, the only answer in that question is a simple repeat of the PHB text that I've included here.
I know the PHB says
Climber's Kit. A climber's kit includes special pitons, boot tips, gloves, and a harness. You can use the climber's kit as an action to anchor yourself; when you do, you can't fall more than 25 feet from the point where you anchored yourself, and you can't climb more than 25 feet away from that point without undoing the anchor.
Here's my question:
Now, I assume that's saying you can anchor yourself anywhere you can reach, i.e. 5ft around you for medium or small creatures. What's not clear is how to undo the anchor. Do you have to be within that 5ft again, or 25ft? Do you have to also spend an action?
For example, if you wanted to use this kit on initiative, would you be spending an action to anchor, then move up that distance, then next turn undo the anchor as an action to move up more? If so, you can't really use it safely during combat to climb.
This is different than the other question because while the title suggests it's about mechanics, the question itself is a different one than this.