@Sacha Jonckers, Thanks for posting in Q&A. Based as I know, the following page can set sign in method. You can click to see if it can access. If yes, you can remove the previous authenticator method and re-add a new one.
https://mysignins.microsoft.com/security-info
I notice you have opened case. Not sure if you have opened case with Microsoft Endra ID. If the above method can't work. You can contact Microsoft Entra ID support to see if you can get help on tis.
https://learn.microsoft.com/en-us/entra/fundamentals/how-to-get-support#open-a-support-request
Hope the above information can help.
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