One other thing I tried is connecting with mobile network rather than Wifi - it's all the same, it doesn't matter whether I connect with mobile or Wifi - it always crashes on iOS, works fine on PC or Android.
I just tried it on my Android phone - I bought it there, started the app, signed in with my child's account, and it worked fine. Luckily, Android / Google Play allow refunds, so I at least got my money back.
I hope that ~45€ I spent this morning on buying additional copies of Minecraft on PC and iOS will help Mojang find the solution 😉
The same is happening for me too. I have tried installing on a different iPad and it's exactly the same symptoms on both iPads.
The workaround you reported doesn't fix anything.
I have two iPads. On the one where the problem started happening there was no Xbox app. On another iPad I didn't have neither Minecraft nor Xbox app. I installed Minecraft first to try to repeat the problem from another iPad. As soon as I installed the app and signed in with the account I use on another iPad, the app froze. Force-restarting the app didn't fix a thing. I installed Xbox app then, and it asked me to sign in - I signed in, signed out, tried Minecraft, nothing changed. Even with Xbox app signed out, Minecraft still signs in using the info it stored. I don't see how two apps could share the same sign-in info anyway...