Hard to say without being there, but that water line goes somewhere after it goes in the ground, you can try just assuming it continues on in the direction it’s bending before going into the ground and go check the next room, or outside and see if there’s any mechanical stuff in that direction.

You can get a stiff pole, or some sort of probe to try to poke into the ground looking for pipes, but you’d have to be careful to not poke a hole in it (or anything else that might be down there.)

Looking at that first picture, it looks like the threads are cross-threaded, so I wouldn’t be surprised if that connector leaks. Based on all evidence presented, it’s probably a not great install job from a previous homeowner. Most of the time those things are connected to irrigation systems, but it could really just be anything that needs a lot of water, but not a constant amount of water. A source to refill a pond? A small pool? An in ground irrigation system? An overbuilt sprinkler system? A really crazy way to just get an outdoor spigot?

Impossible to guess what a random homeowner was thinking 20+ years ago when it was put in.