Hi @Gelos ,
Here is a thread about the same situation from yours, please check the answer:
Authentication app need the Authentication app to sign in? - Microsoft Community
Suggestion:
Regarding to Error message, organization has turned on two-factor verification for account sign-in it can be requires different ways for example, username, password, and mobile device or phone.
Note: this is extra verification because it's more secure than just a password.
You can add new phone numbers, or update existing numbers, from the Additional security verification page.
To change your phone numbers
1.From the How would you like to respond? section of the Additional security verification page, update the phone number information for your Authentication phone (your primary mobile device) and your Office phone.
2.Select the box next to the Alternate authentication phone option, and then type in a secondary phone number where you can receive text messages or phone calls if you can't access your primary device.
3.Select Save.
For disable multi-factor authentication here is reference article.
Best regards,
