Welcome to the ninth circle of, "OMG...are we still using that?", also known as the library inbox.
Yes, it's [still] hosted through Outlook.
Yes, it can be a little painful to get access to.
But, fear not! There is help available. Sort of...if you know where to ask.
First, you'll need to request access to the email@example.com shared mailbox from the Service Desk if you don't already have it.
Access is usually granted in a day or so. Once you have access or if you already have access, you can move onto the next step of this process.
You have access to the inbox. Yay! Now, it's time to add the inbox to Outlook.
Last step! Navigating to the inbox in Outlook.
You may also be able to access some folders from the inbox on your normal inbox home page; however, this will be the path you'll need to get to the shared calendar.