No one knows where Pi ends, so it quite literally did not prove anything. All we can really say is that it seems to be.
And yet the triangles must be drawn infinitely smaller. What happens when we reach Planck Time? How do you draw anything at Planck Time? Try drawing a 3–4–5 right triangle accurate to 0.001 inches. (Hint - what do you draw the lies with?) If that’s too easy, repeat with a few more zeros. Pretty soon, you’re using a scanning tunneling microscope to move individual atoms around, and you’re still not even close to Planck scale.
Yes, yes, we think of these things as “Proof.” Proof occurs in mathematics but not in the real world. When we apply math to the real world, we must operationalize our data. The real world is not always math friendly. Even so, we have no better way of describing, measuring, manipulating, and offering explanations for all we see. Math is certainly King!