If I choose Add Account (+ button) there is nothing to choose from, except some apps that do register accounts on OS level but those are not email accounts. Like owncloud.
There is nothing to choose that allows adding an email account.
On devices with Google apps you can choose “Google” and add google account. But I do not have any Google stuff anymore.
Without google means no google stuff at all. No “google play services”, no google email stuff, nothing.
I use mostly F-Droid for apps and Aurora Store with anonymous login for some things from Google Play, like Yatse.
It does not mean Android with few apps removed or not logged into google account. It means AOSP-like ROM without gapps package.
I checked a device with Google apps. Yes, if Gmail app is installed/enabled then you have “Mail (IMAP)” available under “Add Account”.
But I do not have even google framework/services. Without that it is not even possible to install Gmail app.
That is what AOSP is all about. And also ROMs based on that, like LineageOS. There is no google apps/services/frameworks. Unless you choose to add it. But that is the whole point of AOSP - it’s without all google stuff.