Is there a way to do this via the admin SDK? I am able to do this via the client SDK. I am baffled as to why admin SDK seems to lack many features that clients have. How do I get storage reference using a download URL in admin?
The Firebase Admin SDK for Storage is a fairly thin wrapper around the Google Cloud Storage SDK for that platform, mostly providing auto-initialization of the default bucket that Firebase uses. It does not expose any Firebase-specific functionality, such as mapping from download URLs back to a path in the bucket.
It's a valid request though, so you could file a feature request.