Ask HN: Shared mailbox tools for teams with a lot of mail?

I manage a team of about a dozen who receive many emails per day. These range from alerts/notifications from internal tools, internal work chatter, meeting invites, and external requests that require some action, acknowledgement, or reply.

We moved everyone to a help desk type tool (HelpScout) which has the "assign this task to person" feature that we most wanted, but it's really made for full customer support teams so we are not the biggest fans of it.

Our org has M365 + Outlook which we were on initially, but having so many people with access to one mailbox caused lots of double replies, missed mail, and other headaches.

Any suggestions or similar experiences? I'd like to remove some of the pain out of managing our mail. We make heavy use of automated rules, filters, and workflows to file and categorize mail, but with the variety of mail we still end up spending hours a week on this issue.