The Approved Document is not visible on the Send Email Page in Veeva CRM, Online. The Approved Document is successfully synced from Vault. It is created as a record in CRM and its Status is Approved.
The Record Type of the Approved Document is not an Email Template. Only Approved Document records having Record Type = Email Template appear in the Send Email Page.
Be sure that the Record Type of the Approved Document record is set as Email Template.
CRM Help Documentation: Approved Email Overview