Hi there @iNovikov!
Don here from Shopify. :)
I don't believe that it would be possible to determine a store's ID based on public information such as its domain.
Could you let us know a bit more about what you hope to be able to do with this info, so we can check for any alternate solutions?
Our app work with the Store ID. Usually, the client adds us as a collaborator and we can find store ID in our Partners portal in the "Stores": section.
But right now a client for some technical reason not able to add us as a collaborator. That's why I'm asking this question.
Maybe it is possible to find store id in the network tab in Chrome the developers tool?
Can you explain the solution? Or at least link to it? Generally when you answer your own question it's good etiquette to post the solution for people that come after you and are having the same problem (like me)