While I understand your frustration and the importance of the functionality, the issue with AT&T and SMS messages is outside of Garmin's control. This is not the first time that unilateral changes on the AT&T side have adversely affected inReach SMS functionality for AT&T customers. Note that this impacts all inReach devices, not just the Mini.
This is still a problem. It is March 2020 and the problem is not fixed. Garmin can say it is "outside Garmin's control", however Garmin is still advertising that you can text to any cell phone. If this is not true then stop selling the unit or stop advertising that it will work. This is not a toy that it is simply an inconvenience if it doesn't work! It is very much a work tool for many safety related uses. Garmin, get it together!!! We expect more from you
Please reply to the PM I sent you and I can add you to the Support Ticket open for this issue. More info can be found at https://forums.garmin.com/outdoor-recreation/inreach/f/inreach-general/238987/status-inreach-messages-to-at-t-currently-not-being-delivered
Thank you for posting, I'm sorry you haven't heard back from Product Support yet. Email messages aren't affected by the AT&T issue, so the issue you're encountering is likely unrelated. I would highly recommend checking for software update to your inReach Mini using Garmin Express on a computer, then run the inReach Mini through the inReach Sync Desktop App to sync your account data, then try sending a message to the email recipient again.
This article has steps to sync and update the inReach Mini: Updating the Firmware and Syncing Account Information to an inReach Mini