I've retained "web/app" as it is inclusive of both web push notification and mobile app notification methods. I've cleaned up the description a bit to clarify that browser-based notifications are using web push technology.
I've retained Notification as referring to a notice given by a specific method. For example, a Group Notice delivered by email, versus a Group Notice delivered by web/app notification.
That's a bit pedantic. However where describing the action of Groups.io I've added "sent" for clarity. This fits with the fact that actual delivery depends on the user's system and software, and the user's own choice of settings.
I'll think about the structure, particularly as the page grows to accommodate additional developments.
For now I'm comfortable with having an Introductory section that establishes the terminology, followed by main sections for what the group can control and for what the member can control. Plus the odd-man-out of controls on the user's device rather than within the Groups.io interface.
I think "Group Controls" directly addresses what group owners/mods (GMF's primary audience) are most concerned with: how do we control this beast. I don't want to make them read across a bunch of major sections to glean what they need to know.