Hi Tom,
Based on my research, there isn't currently a setting in New Outlook for Windows that allows emoji suggestions to be disabled, and I haven't found any public information indicating when or whether such an option will be added.
Please note that members on this forum are regular users too and don’t have the ability to change or influence Microsoft product features or design decisions. What we can do is share findings, observed behaviors, and practical tips based on experience and available information.
If you feel this functionality should be configurable, I would encourage you to submit feedback through the Microsoft Feedback Portal, where suggestions can be reviewed by the appropriate product teams. This is the most effective way to ensure your voice reaches the product team and can be considered for future improvements.
Once you've submitted your feedback, feel free to share the link here in the comments. I’ll be happy to upvote it to help bring more visibility.
I hope this information is helpful. Feel free to reply back if you have any questions.