Unable to sign out of Apple Account on new iPhone due to restriction

Go to Settings > Screen Time > Content & Privacy Restrictions > Account Changes, and make sure it is set to Allow. If your device is part of a Family Sharing plan, then it is the Organizer that has control over that setting to prevent you from signing out, and would make no difference what you have showing in your Screen Time settings.

What are your intentions with the members of the plan if you are no longer the Organizer to manage them. Have you tried turning off Family Sharing first. If you have a child under 13 they have to be transferred to another family plan first, since a child under 13 cannot have an account of their own that is not managed by an Organizer. Information about leaving a family group is available here:

Leave or remove a member from a Family Sharing group - Apple Support