Are other cellular features working such as making and receiving cellular calls, and accessing cellular data (wifi off or out of range)?

Have you followed steps for issues with messages after setting up new device?

https://support.apple.com/en-mide/HT204065

I have 4 years iOS tech experience

If the rcs chat thing works great, but if not trust me, try these steps and/or reach out to apple support 800-275-2273 in usa