A cloud-based identity and access management service for securing user authentication and resource access
If your Microsoft account itself is working, but you are blocked only when signing in to Azure because the old Microsoft Authenticator registration is no longer available, this is usually an Azure MFA/tenant access issue rather than a problem with your Microsoft account password.
Since you mentioned that this is a personal account and you are the only administrator, there may not be another administrator who can reset the MFA registration for you.
First, check whether Sign in another way gives you another verification method that you still have access to. If it does, use that method to get into Azure and then update your authentication/security information.
If Authenticator is the only available method and you cannot get past the MFA prompt, you will likely need to contact Microsoft Support and explain that you are the only administrator of the Azure tenant/subscription and have lost access to the registered Authenticator device. Microsoft may need to verify your identity and ownership before helping restore access.
There are recent Microsoft Q&A cases with essentially the same scenario where Microsoft Support/Data Protection assisted with resetting MFA for a personal account that was being used in Azure.
If your personal Microsoft account appears as a guest user in an Entra tenant, and you can somehow access another Global Administrator account for that tenant, the admin can go to:
Microsoft Entra admin center -> Identity -> Users -> All users -> select your account -> Authentication methods -> Require re-register MFA
After that, you can sign in again and register the Authenticator app on your new device.
Because you stated that you are the only administrator, however, the Microsoft Support route is likely the relevant one if there is no other admin account available.
When contacting support, have your Azure subscription/tenant details and proof of ownership available, since they will need to verify that you are authorized to manage the tenant.
I would not create a second Azure account or delete the existing subscription just to get around the MFA prompt, as that does not necessarily restore access to the original subscription.