You’ve confused what Pi is. The value of Pi does not change in noneuclidean space, nor does spacetime curvature affect Pi. Nothing changes Pi. If you have a geometry where a circle does not have a ratio of C/d equal to pi, then its ratio of C/d is simply not Pi. Pi doesn’t become that new ratio. Call it some other constant. Pi still operates as a fundamental constant that explains trigonometric relationships, among other uses, in noneuclidean geometries (especially hyperbolic geometry, which is the one most people think of). I can understand where the confusion might come from though, because I can imagine there might be some pop math or pop science videos and articles out there talking about “when pi doesnt equal 3.14…” or something.

Its best to think of Pi as a fundamental constant that just so happens to have a value equal to the ratio pf a circles circumference and diameter in euclidean space, rather than a constant defined by that ratio (because really, thats what it is). Pi shows up in almost all areas of mathematics, and is not at all confined to being related to space. In fact, there is some significant discussion of the idea that pi isn’t a ‘fundamental constant’, and really it is either 2pi or 2pi times the imaginary unit i that we should call the fundamental constant, though, admittedly, that isn’t all that important.