Is there currently such a thing as a Web interface for viewing files in a git-annex repository, and being able to carry out git-annex operations like get/drop?
There are several different Web-based file browsers available, which work fine on a git-annex repo but don't let you do annex operations. I could also run a generic WebDAV server and client, but that has the same problem.
The eventual use case is to expose the interface behind an HTTPS reverse proxy that will handle authentication, so no authentication functionality is needed.
I don't know of such a thing that is explicitly web-based.
See file manager integration for how to set up several file managers to be able to do get/drop. I don't see any reason some web-based file manager couldn't have similar hooks to the ones used there.