Is my phone using T-Mobile or AT&T?

I have T-Mobile for internet (with the Arcadyan gateway) and my phone uses AT&T. Lately internet on the phone has been extremely slow, many times I try loading a page and get nothing. If I go back and try again it’ll usually load. Speed on my desktop is quite a bit faster than the phone. The phone is a Motorola android version 11. I regularly shut the phone and gateway down and restart, but it doesn’t help.

I’m confused as to whether my phone is using T-Mobile or AT&T for internet, so I’m not sure where to start researching the problem. I have wi-fi calling off as it was causing problems with calls (lots of static, couldn’t hear them, they couldn’t hear me). Also if it makes a difference the network types I have to chose from are LTE, 3G and 2G (I know, not great...). It’s been on LTE all along - when I tried switching to 3G I lost internet altogether on the phone. Mostly I need to know which company is providing internet on my phone. Thank you!