T-Mobile is the only internet available here. And from what I can remember, they use the same system as AT&T, so you might actually get service, if you had service with AT&T.
AT&T and T-Mobile run separate networks. They use similar technology but have their own "cells", networks, etc. So even if AT&T works great, T-Mobile in the same area could be a total bomb, or vice versa. It's common in some areas for the mobile phone operators to share towers but they each put their own equipment on the single tower. (Some locations limit tower placement so the companies share). I have heard that in some remote areas the companies have agreements to provide service for each other's customers in a non-roaming manner.
In the old days, AT&T and T-Mobile were both GSM providers, meaning the technology that they both used was based on the GSM standards. That meant they used SIM cards and unlocked phones could usually work on both networks with a SIM card switch. verizon and US Cellular and Sprint used CDMA technology, which was different. By the time we got to LTE based systems (at the latest, may have been earlier with so-called 4G systems) everyone was using a variant of the same technology. LTE uses GSM style signaling and administration so Verizon and the others started using SIM cards but the actual data signals were new tech in any case. But the control layer was based on GSM. There are variants of LTE and 5G etc so one carrier may use a slightly different version of LTE or whatever but it's all basically the same (at least in the US and Europe -- China I believe has an LTE based on a different principal). You can see this when looking at all the supported "bands" and "service" for a given phone model in the spec sheet.
(T-Mobile started life in the US as VoiceStream before Deutsche Telekom bought it and rebranded it to T-Mobile. which is analogous to the European T-Mobil, and which has since been divested by Deutsche Telekom and is its own company. There were other GSM based systems in the US like Omnipoint in the North East which were bought up by T-Mobile as they expanded their network early after they became T-Mobile. I had a VoiceStream phone around 1997 and when I moved to New Hampshire had an OmniPoint phone which became T-Mobile. Moving back to Utah I got on T-Mobile here and have a number since that I took to AT&T, back to T-Mobile, and now on Mint Mobile. My daughter, when we got her a phone a few years ago, was given a number from the old original Voicestream series of numbers and it is very very close to what I remember my old VoiceStream number was.
Regarding Mint Mobile. It is a pre-paid system only and is a MVNO. They don't own or run any of their own cell towers etc. They buy bulk minutes and data from one of the physical carriers like T-Mobile, AT&T, Verizon, etc. In this case Mint Mobile uses the T-Mobile network, though they have their own SIM cards etc so T-Mobile knows you're a Mint Mobile customer and can down or upgtrade your service based on that and what they've agreed with the MVNO. Mint Mobie was actually bought by T-Mobile so now they're just a subsidiary and not a separate MVNO company. They're still run separately. For me, paying a year at a time, I pay less than 1/2 of what I was paying before for our grandfathered T-Mobile plan. Other MVNO are the other carriers you see that aren't AT&T, T-Mobile, or Verizon, or one of the other small local physical carriers that might exist. MVNO can be partnered with just one physical carrier, or they can use multiple ones. Examples are Xfinity Mobile, SimpleTalk, Virgin, etc. MVNO means mobile virtual network operator.
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"aint I a stinker" I didn't notice any savings, but with outside temperature variations it's hard to tell.
