Welcome to the Airtable community!
It would be great to have some way to identify the base/table from a shared view/form. Unfortunately there currently is no good way other than looking through all the tables/bases. In part this is for privacy reasons. These shared views are designed to be made public, and thus you don’t want any private info (including the base ID)) associated with the public url.
It would be super nice if Airtable added a feature to a workspace where you could search for a base/table by shared url. Feel free to contact support to make the suggestion. Be sure to explain your use case.