Google isn't just shutting down the consumer version of Google+ as a response to privacy concerns. The company is gradually rolling out a change to its developer tools that will give users much more control over privacy permissions for their account data. Much like permissions in recent Android versions, you'll get permission requests one at a time for various services. You could grant access to Drive, for instance, but turn down Gmail or Calendar permissions.
The changes will start reaching new users in October, and should extend to existing users in early 2019.
While Google didn't say as much, the clampdown appears to be a reaction to word that its previous policies let third-party apps scan Gmail inboxes without much clarity for users. This change should make it clear what apps really want. Google is also using the fine-grained control as a way to promote better explanations to users. While it's not mandating elaborate descriptions, it's hoping the item-by-item permissions will encourage clearer dialog and prevent any rude surprises.