AppleTV "Channels" - Help with how to watch, manage, etc.

I'm soooo tired of these streaming services and how unintuitive they all are...

I signed up for CBS All Access through the AppleTV app. It took me a frustrating half hour of trying to log into the CBS All Access app before I realized that a CBS-AA subscription via their app is different from a CBS-AA channel subscription via the AppleTV (which is also apparently different from a CBS-AA subscription using iTunes?).

My question is... Can I watch stuff from this CBS All Access channel on a web browser or do I HAVE to be on a mobile device using the AppleTV app? I found the tv.apple.com website and logged into that, but it's literally just a layer-cake pile of AppleTV Originals with no navigation or search capability, and no channels.