Using the embedded sdk and oauth you can load your app into shopify admin as an embedded app. It’s literally an iframe. Shopify’s example app is a Rails app. No reason it couldn’t be a phoenix app.
From my understanding app bridge is just a library that allows you to utilize the shopify ui and actions instead building them yourself. For example if you wanted to show a confirm modal you can use app bridge to show that modal using shopify’s already built ui and subscribe the the actions. You don’t have to actually build your own modal. You may call the actions from javascript (which makes sense) but the app does not need to be a react app or any type of SPA.
I don’t want to get too far off topic regarding @wlminimal original question. Obviously shopify provides the needed tools and documentation. To meet specific app requirements it’s probably best to consult the docs. I just wanted to point out polaris and react are not required. You can build a server side rendered elixir/phoenix app with a sprinkle of js and use oauth. Embedding apps is also not a requirement.