Unfortunately, there isn’t any documentation for a new user sign-up approval flow. However, you could definitely make this work with the Send Email Invitations for Application Signup approach.
From what I gathered from your flow, steps 1 and 2, sound to me like you have a mechanism to approve users, which an Admin then sends the email invitation to them after approval. From here, you would need to send the email invitation to your users to sign up on the third step, where they can set their passwords and log in to their account.