Aligning a webapp with the API

I am considering redesigning a web application so that it is structured the same way as the API. The same URL would take the user to an application in a browser, or a corresponding API endpoint if used programmatically. That could work by checking the request headers.

The goal is to improve discoverability or exploration of functionality. Many of our users might want to use the API programmatically. They could explore the API using the user interface. For a detailed definition of the API, there is SwaggerUI already.

Do you have any experience with this approach or advice? Any opinions?