A website mailbox works best when someone knows who monitors it, who can reply and what happens when they are away.
List the addresses you need, such as a contact inbox for visitors and a billing address for provider notices. Decide whether each address needs its own inbox or can forward to an existing team mailbox. Send a test from an external account and confirm replies use the expected address.
During a handover, document who owns the email service and where to update its DNS records. Keep a copy of the settings and test website form delivery separately from direct email delivery.