Same here, it must depend on how the additional mailbox is added. Mine is under "Shared with me" which was added by IT and I can't add that email account to Favourites. Adding the email account using the email address and password should work.
If it's a shared mailbox in a business tenant, chances are it will have been shared by IT - that's certainly how we do it. It then appears, as you say, in the 'Shared with me' section. If an account appears in 'Shared with me' there is no option to add the account (or folders within the account, such as the inbox) to the favourites.
Adding shared accounts using an email address and password would be very bad practice as it would mean sharing credentials for accounts (that's a big no for us), and would mean that MFA would have to be disabled on the account. The account would therefore become a significant security risk. The accounts to which our shared mailboxes are attached are all disabled so that they cannot be logged into directly, and sharing is done by means of adding the required users to the mailbox permissions in the M365 console.