I'm actually pretty surprised at how well all the different versions seem to work. However, when using a web browser to access my images, I can see editable fields for title and caption but not keywords. The keywords are there and are searchable but can't be modified in any way.
Am I missing something? Seems this would be a key feature.
You are right, the ability to add keywords does not seem to be a feature of Lightroom.adobe.com at the present time. (I think) up to just a few weeks ago that website was more an extension of the desktop Lightroom than it is now, but with the introduction of the new cloud-based Lightroom CC the role of that website changes significantly in many respects. If you would like to make a feature request, here is the website where doing so is more appropriate: