By definition if we can observe it (either directly or indirectly via the effects on stuff we can directly observe), it's part of the observable universe.
If it's outside the observable universe then by definition it has no observable effect. Until technology improves to expand the observable universe to a degree that we can observe it or it does something that allows us to observe it (which adds it to the observable universe), then it doesn't really matter to us.
In other words: If it's not part of the observable universe, it doesn't matter to us because we can't possibly know anything about it. However as soon as we discover something about it, it becomes part of the observable universe and now we can care about it because we know of it.
No, it does not depend on our technological capabilities. The observable universe [0] of a point is defined as the space from which it is theoretically possible that a signal can reach it. So: every point in space has its own observable universe and it is not dependent on any technological capabilities.
Edit, excerpt from [0]:
βThe word observable in this sense does not refer to the capability of modern technology to detect light or other information from an object, or whether there is anything to be detected. It refers to the physical limit created by the speed of light itself.β
Lol, no. "Observable universe" is not a philosophical concept; it's a physical one with a precise definition: those parts of the universe that fell within our past light cone.
If it's outside the observable universe then by definition it has no observable effect. Until technology improves to expand the observable universe to a degree that we can observe it or it does something that allows us to observe it (which adds it to the observable universe), then it doesn't really matter to us.
In other words: If it's not part of the observable universe, it doesn't matter to us because we can't possibly know anything about it. However as soon as we discover something about it, it becomes part of the observable universe and now we can care about it because we know of it.