I faced the similar issue when a client was considering Epicor CRM and outlook integration was essential.
The client was on 365, so I created a VS app using MS Graph that I deployed to 365.
The app looked in a designated mailbox (e.g. sales) and then matched the ‘To’ email address of all the emails to an email in Epicor and then created a CRM call for the customer/ contact and attached the HTML to a UD field on call entry call (EmailText_c) using the Epicor API.
Once the email had been loaded into Epicor, the email was moved to Archive.
Ultimately, the app would be scheduled to run periodically.
Finally, I had to customize the CRMCallEntry to display the HTML using CEF (see CEF To Load Documents on Order Entry Screen - #2 by josecgomez)
The idea worked in principle, but ultimately a tighter integration with Outlook was required with calendars etc, so the client moved on to a more sophisticated CRM system.
Overall though, it was a good exercise into understanding the working of Azure and Enterprise apps and certainly an option if you just want to capture customer emails and are running on 365.