This is exactly what the “Get a link to my development environment” link is for! It gives you a URL that will access whatever version of the app you currently have open in the editor. You can use it to open the app in a browser, or to access HTTP endpoints as you’re editing them.
(Of course, you can do this by hand if you want - you could create a new environment and point it at the branch you’re currently editing, and move it if you switch to editing another branch. The development environment just automates this for you!)
The relevant docs are here: