Managing personal Outlook.com account settings, security, and privacy
Is 2-step Verification turned Off on the said account? If Yes, you could try using the automated account recovery form since the password reset is not successful. The form applies if 2-step verification hasn't been enabled. Below is Microsoft's guideline for using the form.
https://support.microsoft.com/en-us/account-bil...
Otherwise, you'll have to wait until the SMS service issue is fixed by Microsoft as codes aren't arriving for many users at the moment.
Just so there’s no misunderstanding, this is a user-to-user support forum. We’re users just like you helping other users. We do not work for Microsoft and have no access to any user account so there is nothing we can do or check from within the forum. We have no input on Microsoft’s policies, procedures, or design decisions.