@Konstantinas Grigalaitis, Thanks for posting in Q&A.
For your issue, here are some suggestions you can refer.
Q1.is it possible to remove the phone number from this user?
A1. We can go to the https://myaccount.microsoft.com/ website and login in using the account and click UPDATE INFO under Security info to see if there exist the previous phone number and we can try to remove it, after that we can check if we can use the account to login in using WHfB without phone number authentication.
Q2. How can I make an exception to Win Hello on this account?
A1. If we enable Windows Hello for Business during enrollment, we cannot make an exception to Windows Hello for Business on one specific account, because we can only disable it for all users and device, however, we can first disable it and enable it via Account Protection policy, then we can exclude one specific account. If we enable it after device enrollment and configure it through Account Protection policy, we can create a user group containing the account to exclude from this policy, after that the account will not apply this policy.
https://learn.microsoft.com/en-us/mem/intune/protect/identity-protection-configure
Hope above information can help you, if there is any update, feel free to let me know.
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