but when I try to work with a shape from my library both AI and PS say that the shape isn't directly editable and I can only place it. What application can truly edit these shapes?
As the previous poster commented, you CANNOT edit shapes created in Adobe Shape in Photoshop CC. You also can't seem to download or save them elsewhere, so why this app exists is beyond me.
I've just started playing around with Adobe Shape myself. It looks like you can't edit the item in Photoshop. It's just a non-editable Adobe CC Library object and you get a warning saying that it can't be directly edited in Photoshop, only placed. However, if you go into Illustrator and place the object into document, you can then easily edit the resulting vectors just like any other vector object. However, the original Shape generated object isn't affected, only the vector object currently sitting in your Illustrator document.
What you can do at this point, is to resave the edited vectors as a new Library object should you want to sync it to the cloud and share it with other apps. I don't think that this will allow the shape to be used in Adobe Shape or not though.