You can only set an Out of Office Message/automatic reply for shared mailboxes via Outlook on the Web.
- Open Outlook on the Web.
- Select your profile icon in the top right corner and select Open another mailbox.

- Enter the name/email address of the shared mailbox and select Open.

- The shared mailbox will open in a new browser tab. Follow steps 2-6 in the Outlook on the Web section to configure automatic replies for the shared mailbox.