On-prem shared mailbox access in hybrid Environment

There is, but it depends on the permissions. Full access is supported cross-premises, delegate/folder-level permissions require additional steps. Automapping is not supported, which is why the mailbox was removed from Outlook.

It's usually best to move them (together with the corresponding user mailboxes) to ExO. See for example: https://learn.microsoft.com/en-us/exchange/permissions#mailbox-permissions-and-capabilities-not-supported-in-hybrid-environments