Can a Non embedded app that follows oauth flow of shopify get publicly listed after review?

[tanmay07]

I would like to know whether it is mandatory to create an embedded app in Shopify to have it reviewed and publicly listed. Can a non-embedded app (server), which adheres to the Shopify OAuth flow by redirecting the user to a redirect URI generated by a Shopify library, such as 'shopify-api-js,' also be publicly listed after undergoing the Shopify review process?
I am seeking this information because I intend to develop a non-embedded app. My application (frontend) currently offers the option to create a user via email and password. I also aim to onboard users onto that app through Shopify, providing additional functionalities to merchants.