I use Zoho Desk for tracking support tickets. It’s free up to I think 25 users. I deal with the emailed to me case by opening a ticket and copy/pasting the email into it.
I second Zoho, Zoho everything. I run a 1 person company and love Zoho. I think their mail is far superior to gmail, their office apps are superior to gsuite, invoicing is great too.
I don't use Desk or many of their other apps, but they have them, and are integrated with each other. In a way integration is better than automation. Because it is integrated in one platform it is available to all applications. I don't know if that counts as less automation or more automation but I know it means less time spent on it for me.
I have no affiliation with Zoho beyond being a happy customer.