Dear Julie,
Thanks for your reply.
New Outlook can't support Focused and the Other feature while you access the share folder or mailbox :(
Focused Inbox for Outlook - Microsoft Support
The Focused Inbox REST API provides Microsoft 365 mailbox message classification and training to help users sort their email efficiently. However, this API isn't supported for the Microsoft 365 Shared mailbox. Outlook for Windows currently displays "Focused Inbox" hints for shared mailboxes. This is unexpected behavior. Microsoft is aware of the problem, and this article will be updated after changes are complete.
We do understand it would be more convenient and suitable for your daily work, but as New Outlook is still working on product features development and in improvement. Please waiting for Outlook product team release this feature in New Outlook and New Outlook for web.
As a workaround, you could use Simplified and Classic Ribbons in Outlook for web or Classic Outlook desktop app.
Thanks for your patience and understanding. Have a good day!!
Best Regards,
Microsoft Community