Mail contacts have long been used by Exchange organizations to provide an identity for external people. Contacts show up in the GAL to make it easy for users to send messages to external people and they can be included in distribution lists. The downside is that mail contacts are only available to Exchange Online. Perhaps the time is right to consider switching focus to Azure AD guest accounts? We explore the option here.
You can use a public folder to store and share global email contacts, but a better approach is to use Exchange mail contacts. These objects show up in the Exchange GAL and OAB and are available to all Outlook clients (and some third-party clients too).