How to sync mail across devices

I have an iPhone, two iPads, and a Mac, and I use Apple Mail on all of them. The trouble is, the email doesn’t sync across any of the devices. For example, if I want to delete an email, I have to do it on each device ... four times. This doesn’t seem to be an iCloud issue, because things like Photos, Notes, Contacts, Calendar, etc sync just fine.

I have three email accounts - Gmail, iCloud, and Comcast (my primary account). Only Gmail syncs across all devices. I’ve been looking into this all afternoon, and checked many things as I went, but everything seems to be ok.

I really don’t want to switch to another email client, so I’m hoping that someone can help me.