API Access app in App store

Shopify App Store
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1

I want to offer our API app on Shopify App Store. Currently we have our clients use the private application method to get API Access to pull orders, send shipping data, update inventory etc. We want to put our api app on the shopify app store and do an OAuth 2.0 process to get access and make it easier for our clients.
We do not have any UI components to be shown on the Shopify webstore. We are just api access.
Where to go? Where to start?
Ideally we would send our clients to the app link in the app store where they would click the app go through the OAuth process and we would start handling their orders. Or they would start on our website and go to shopify login etc.

We are specifically looking to make an API app.

2

So you can’t have an app on the app store that doesn’t have UI.

3

Is there an alternative easy sign up process for API access?
We have a setup in Walmart, Amazon, Ebay, etc where we people can sign up to use our app for managing their orders.

The goal is for an easy sign up process. We have to do a lot of holding using the Private Apps and Dev Dashboard apps.