There's currently no way to get a list of shared mailbox members and their permissions for the mailbox. This can only be done via PowerShell. The ability to get this information via Graph would be useful. Since there is no way currently to distinguish a normal user from a shared mailbox via graph, perhaps (hopefully!) this change would involve a new top-level sharedMailbox object, a property of which is the member list.
Our app maintains a shared mailbox subfolder for each mailbox member. Currently, the only way to determine the members and detect membership changes—so we can create and delete member folders—is for our customer to manually run a PowerShell script. This is not great for any customer and especially those with often-changing membership lists. It would be far better if our app could use its access via Graph to check the mailbox member list periodically. (Ideally, there would also be a webhook for member list change notifications.)
Since our app requires each user to have Full Access to the mailbox, we would also need to know each member's mailbox permissions.