We have been developing an application using Odoo as a backend only. The  end user of the system is not aware that the system is built on top of odoo. We are using Oddo v18.

It is a custom application with features owith features of CRM, Discuss, and Marketing Automation. It is being developed using the MERN stack. 

We need to provide two way sync of email i.e. if any email is being sent using our system (behind the scene odoo) then that should be visible in my mailbox (gmail/outlook etc) and if any email is sent using my gmail/outlook then that should be visible in my application (odoo). Flow of the application should be just to ask users to provide credentials of mailbox and we should be able to achieve tow way sync.