The Oort Cloud is not gravitationally attracted enough to the Sun to form into a fairly thin disk, like the inner Solar System.
Thus, comets originating from the Oort Cloud can come from roughly any orientation (inclination to the ecliptic), and many even have a retrograde orbit.
By definition, a hyperbolic orbit means that the comet will only travel through the Solar System once, with the Sun acting as a gravitational slingshot, sending the comet hurtling out of the Solar System entirely unless its eccentricity is otherwise changed.
In the list below, a number of comets discovered by the SOHO space telescope have assumed eccentricities of exactly 1.0, because most orbits are based on only an insufficient observation arc of several hours or minutes.
[1] Solar System comets may also become interstellar after close planetary flybys like in the cases of C/1980 E1 (Bowell) and C/2024 L5 (ATLAS).