We are looking to build a Shopify integration for our tool. We want to be able to pull Shopify data for verification and analytics purposes via the admin API. We are happy to have users go through an OAuth flow, that would be initiated from our web app and completed via Shopify. And we are happy to appear as an app in Shopify Admin.
However, this tool is not standalone and so we don't want it to appear on the Shopify App Store, we only want it to be installable via our web app.
I've previously used apps like "Uncapped", that achieve this, however I'm not sure which distribution channel to use in this case. It looks as though it is either a "Public" app that must appear on the App Store or a "Custom App" and only installable on single merchant sites.