Organizing Shared Mailbox to Direct certain senders to subfolders

Shared mailboxes support a folder structure in the same way a "regular" mailbox does, you should have no problems creating additional folders or subfolders. As for moving messages to (sub)folders, that's what Inbox rules are for. To manage rules for a shared mailbox via Outlook, you need to first add it as an additional account thought, which is done via File > Add account and entering the credentials of a delegate (with full mailbox permissions) when prompted. If you need step-by-step instructions, check here: https://www.michev.info/blog/post/3567/how-to-add-a-shared-mailbox-as-additional-account-in-outlook-2022-version
To do the same via OWA, click your profile picture in the top right corners > select Open another mailbox and point to the shared mailbox > access Options and configure rules therein.