It'll show "Sign Up" because it can't detect you're logged into Joomlapolis. Login to Joomlapolis then click Refresh in the bottom right to see if the JSONP request can pick up your login access. If it can't you'll need to download it manually and install it manually. We're working on implementing a Site Key system so we don't have to depend on JSONP working. We can't deliver build releases through Joomla update as Joomla doesn't support metadata in versions (we're trying to figure out a way to fix this too).

If it fails you'll unfortunately have to update manually. If you don't want to be notified of build releases you can turn off plugin version checking in CB > Configuration > Integrations. There's about a dozen different reasons why the JSONP request fails to see why you're logged in which is why we're going to replace it with a site key system.

I don't really get why, while all other plugins can, CB can't be updated from the Joomla admin, BUT at least it should be straightforward (one click download) AND not require account creation or login in any way.

Those extensions don't release updates as rapidly and often as we do. To do this we need to use semver metadata in the version. That's what the +build is in the version. It's a build number generated at time of build and release. Joomla version checker can't handle +build. This allows us to push fixes and features extremely quickly. We're working on a solution to see if we can workaround this in a later release, but we don't have one for now.