The answer
Nameservers determine where the active DNS records for your domain are managed. Changing them does not copy existing records automatically. Prepare website, email and verification records at the new destination first.
What to do
Save all existing DNS records and fully prepare the new zone.
Open the domain and Nameservers tab in your account.
Enter the complete assigned nameserver names and save.
After the change, check the website, email and active delegation.