If you performed a reboot, plus removed/visually checked for lint etc/put the Sim back in but this didn’t fix it, I’d call the carrier asap. If you’re paying AT&T then it is on them to make their SIM card work. A smartphone is a handheld Wi-Fi device without the Sim. And the Sim is a Carrier device, it’s what makes a phone part of and capable of using a cellular network.
But it definitely wouldn’t hurt to check out the applicable Apple Support document:
https://support.apple.com/en-us/HT201415
I see AT&T which, I’m pretty sure-ish, you can (same size) put into another iPhone that is unlocked or locked to AT&T. If you have such a device nearby and can test this, and get the same results, the Sim is bad or the carrier has some issue with the Account. But I’d stick to calling the carrier support.