Hello, thank you for reaching out to Microsoft Q&A.
Please note that the option to 'Add Phone number' is missing on the 'Manage how you Sign in with your Microsoft account' page, this is a widespread issue.
It appears to be affecting multiple users and is likely related to a backend or server-side change on Microsoft’s end, rather than a problem specific to your account or device. I recommend waiting 48–72 hours, then checking again to see whether the option has been restored and the issue resolved on the backend.
Recent discussion thread for your reference:
How to add phone number in Account Info add phone is missing
Also, I do not see the option to add a phone number on the page. To add your phone number to verify your Identity, go to https://account.live.com > Security > Manage how I sign in > Add your Phone number.
The discussion thread is in English. We recommend using a translator if required.