While our lovely AI assistant is correct about the solution, the steps he presented are not. Adding an additional account in Outlook will indeed allow you to set the shared mailbox as default in Outlook, but to do that you need to use File > Add account > enter the shared mailbox address > (most important step) enter your credentials when prompted. For this method to work, you must have Full access permissions. Additional details and step-by-step instructions can be found here: https://www.michev.info/blog/post/3567/how-to-add-a-shared-mailbox-as-additional-account-in-outlook-2022-version
If you have multiple accounts in Outlook and you want to set the default From address across all of them, don't forget to set the newly added account as default, and also toggle the "Always use the default account when composing new messages" setting under File > Options > Mail > Send messages.