Embded app or shopify theme app extension/proper way to work with 3rd party API - oauth way

Hello. I’m trying to figure out how to properly expose my application in the app store.
My application works according to the following scheme. I recognized it as a theme app extension, but it seems to me that I made a mistake and am doing something wrong. Maybe I should publish it as an embedded app after all.

The main problem is that I transfer the oauth authorization data from the nodejs cli template to my api on another server and from there I make requests to the Shopify admin api. It seems that this is not entirely true and also the session token has a limited lifetime (although I do not know what). Therefore, it will not be possible to update it and my requests to the admin api will not work.

I would also like to understand whether it is possible to use public links to the nodejs cli template where oauth authorization takes place. For example, so that I can access it from the client code of the store itself. Because now, precisely because I did not understand how I can access the nodejs cli, I make requests to my backend on another server.

Also I can’t figure out which links I should specify on the app’s publishing settings page.