The old-school mailing lists are going away, but Discourse will mail you essentially the same notifications. Here’s how to get them.
Click your avatar in the upper right, select Preferences (the little person icon) and then Preferences (yes, again, this time the little gear icon) on that menu. You should get a screen something like this.
For the second option, you either want “only when away,” or “always.”
Next, pick Categories under Notifications. This is where you’re going to set your watched categories. Blog Entries is the equivalent of getting emailed copies of the blog posts (though there’s no weekly summary, as far as I can tell). Announcements is the equivalent of the New Product Announcement newsletter - also no weekly summary, but I’ll only be issuing weekly (or less often) announcements so it’s the same effect.
Of course, you can tell it to Watch any other category you want.