So I feel like I understand how both these laws work however it seems like Ampère's law will find the strength of the magnetic field at a point (the point is taken as $z$ in this example and the red lines represent the contour of the magnetic field):
And the Biot-Savart law essentially finds the magnetic field at that point that is due to the current in the whole wire (where the red lines, in this case, represent the unit vector of the current at distances infinitesimally small in the wire):
Now my questions are, why does Ampère's law often apply to an infinitely long wire and the Biot-Savart Law apply to a short wire? Wouldn't it make sense for the Biot-Savart Law to apply for situations where there is a long wire since the current all the way through the wire would affect the magnetic field at a point $z$? And in that case, why would you ever use Ampère's law?
I feel Ampère's law would be innaccurate as it only represents the magnetic field directly perpendicular to the current wire at a certain length $dl$. But surely more of the wire would affect the magnetic field at point $z$ so how can you ever use Ampère's law? I feel that the Biot-Savart law makes more sense in every scenario, please help.