T-mobile's claim is that by 2024 their customers will get emergency satellite connectivity on their existing handsets, even cheap $200 ones. They might need to be new $200 handsets in order to get the software support, but the hardware support is supposedly there already. The specific language T-mobile uses is the "vast majority of smartphones already on T‑Mobile’s network" which sure sounds like it includes $200 phones. With the help of Starlink, T-mobile is going to put cellphone towers in space, pointed down, and your existing cellphone will be able to pick up the signal and the satellites will be sensitive enough to hear the cellphone's transmissions.
T-mobile's service will be limited to various forms of texting and possibly also Twitter, which is used by many emergency departments to broadcast information, which is slightly different than the iPhone's offering of dire emergency service coverage. Still doesn't replace AM radio use cases though.
No, I don't think $200 phones are getting satellite connectivity.