What's the messenger icon that appears next to my email on the mail app?

That's not the Messenger icon, that's the Offline indicator.

A lightning bolt icon  next to an account’s mailboxes in the Mail sidebar and at the end of the Favorites bar indicates the account is offline.

click here ➜ Take email accounts offline or online in Mail on Mac - Apple Support

Should have refreshed before posting the reply. Guess I took too long to find the right KB article.

I see two icons. One is the mailbox icon and the other is the indicates the mailbox is offline.

Take email accounts offline or online in Mail on Mac - Apple Support

Phil0124 wrote:

Should have refreshed before posting the reply. Guess I took too long to find the right KB article.

That happens to me all the time! ;-)