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 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 and then checking again to see if the option has been restored and the issue has been resolved from the backend.
Recent Reddit article for your reference:
https://www.reddit.com/r/MicrosoftRewards/comments/1ryb3x7/cant_add_phone_number/
Standard Disclaimer: This is a non-Microsoft website. The page appears to be providing accurate, safe information. Watch out for ads on the site that may advertise products frequently classified as a PUP (Potentially Unwanted Products). Thoroughly research any product advertised on the site before you decide to download and install it.'