How can I restore deleted archived emails from an iPhone backup?

MS 365 email messages are not part of the iPhone backup. They are sandboxed for security. That's how Exchange accounts work.

Have you logged into your account on the web to see if they are still there or recoverable?

This is something you'll have to take up with Microsoft.

I need to know this too. I was being nagged by the Mail app to enter my 365 email password. When I did, it deleted THOUSANDS of flagged and organized emails from my inbox and my Deleted items. I forgot to do the restore of the deleted items on Outlook and now the option is gone. No idea how it deleted permanently without my permission and no one can tell me. Thousands of potential customers and years of organizing work gone.

Contact your email provider. Unless your account was set up as a POP3 account, which is highly unlikely, your email was never part of the backup. Any backups would have to take place on the mail server.