What controls the text preview in notifications? I am new to Android (on Samsung S7 now), and trying to understand the basic (so that I can drill more into details later).

My notifications (emails) show the sender and email title, but not the email body preview (the iOS lock screen showed a few lines of the email body). I have "content preview" enabled on device settings.

What controls the amount of information displayed in previews? 


Is this a device/ROM setting that all notification apps have to adhere to? 
Is it the underlying email client application?
Or is it the notification application itself?


In other words, in order to see email body preview in notifications, should I be looking for a different email client, different notifier, or different ROM?
Everything in the notification is set by the app that created it. So in the case of your email, it's the email client.

Note that in recent Android versions, you can expand most notifications by pulling down on them with two fingers. In Gmail, for example, if you have a notification about several emails, you can expand it from "3 new messages" to show the sender and subject line for each. If you only have one new mail, the default layout shows the sender, subject line, and first line, but the expanded form shows a few extra lines of the content.