I notice you are registered in the UK, but you are currently signed in to the US discussion boards.
Have you tried changing your phone number on ebay.co.uk?
If you are changing to a new mobile number, try changing your number using the eBay app. Or try using a different device -- I was able to make the change on one computer but not another on a different network.
For some other possible suggestions, see this thread on the US discussion boards:
https://community.ebay.com/t5/Technical-Issues/Can-t-change-my-phone-number-on-file/m-p/31687830#M82...
