As you already know the Microsoft Authenticator application has been primarily used for multi-factor authentication (MFA).
Over the time the Authenticator app has evolved to allow you save your passwords, forms information or even deliver a password-less experience during authentication.
Well, you can now also use the Authenticator to change your password.
To do so, just launch the application and select the account (if multiple) you want to change the password and choose Change password
This will then open the Self Service Password Reset page. Doing so you will be automatically identified and authenticated to change your password.
Off course this requires your administrators have enabled the Self Service Password Reset and your account is authorized to use it
From the same location (the selected account), you can also change your Security details
Because you are editing sensitive information to identify you, you will be prompted for MFA