If you want your app to embed the Meeting in AA/NA Live! (previous implementation), you should definitely use the Meeting SDK. If you want to kick out to the Zoom app, you don’t need to get reviewed — because your app wouldn’t have access to the user data available in the Meeting SDK.
You don’t need to be published/publicly listed on our App Marketplace; the app could be unlisted/undiscoverable on the Zoom App Marketplace. You’d have something like a “connect your Zoom account” button in your app and a user would be shown an app install page, then be redirected back if successful. (And yes we think you should share your honorable work with the world if that makes sense to you).
If you want to use the Meeting SDK, your app just needs to go through App Review to join meetings external to your own account (meetings hosted by users not on your same account). If you were building AA/NA Live! for people on your own account, we don’t need to review. If you allow users to download the app from the Play Store and join any meeting (say, connect a calendar or have people input the ID/passcode), your SDK key needs to pass through review in order to join those meetings.