One more data point: Feedback Assistant now shows "Recent Similar Reports: More than 10" on FB24404901, so the current wave (see also FB24034392 above) is clearly widespread. Our case rules out everything client-side: it reproduces team-wide (a brand-new App ID fails identically), on iOS 15 through iPadOS 26, on multiple devices and Apple IDs, with scoped and minimal requests — while the same devices and accounts complete fresh Sign in with Apple authorizations for other teams' apps normally.
If you're hitting this too, please file the Feedback per thread 801173 and post your FB ID here — more linked reports should help prioritization.