The free inflight messaging that T-Mobile offered was just a "free offer for customers of T-Mobile" deal on services provided by an in-flight internet provider. Basically a "free doordash premium subscription for chase sapphire reserve customers" type of a deal.
Regardless if you are a T-Mobile customer using that deal or not at all, you join the in-plane WiFi AP, it goes to the captive portal, and there you get options like "tmobile customers offer", "single flight pass", and "monthly flight pass". Once you pick your option and get through it, you have internet access. And regardless which option you went with, you get the exact same type of internet connection as everyone else on that flight.
From what I've personally seen, it was done through GoGo Inflight Internet[0] heavy majority of the time.
0. https://gogoair.com