chore(openapi): regenerate the spec for the badminton sport type

The badminton mapping added the enum member in the Zod registry and left the
generated spec behind, so the drift gate failed. One line, `- badminton`.

Third failure this branch revealed in sequence: the formatter hid a red test,
the red test hid this. Each gate only runs once the one before it passes, so a
single unformatted line kept two real problems invisible.

docs/api/openapi.yaml

@@ -3363,6 +3363,7 @@ paths:
                           - hiit
                           - dance
                           - golf
+                          - badminton
                           - tennis
                           - basketball
                           - soccer