An update: the problem turned out to be eSim confusion. When we purchased the phone, it had the wrong phone number on it. Our carrier (AT&T) store fixed it by adding the correct number, replacing the eSim on the iPhone11 with a physical Sim with its original number (that had been put on the iPhone13 Mini by mistake). As it turns out, the tech in the store neglected to delete the original eSim (with the incorrect number) from the iPhone13 Mini, so it kept on searching for a cellular signal that it wasn't going to find. We'll continue to test for two days, but it appears the problem has been fixed.
Our initial call to Apple was unsatisfactory, as the CSR's response (after supposedly talking to an engineer) was that we would just have to live with it in the face of a low signal. We kept trying to tell her that we consistently have 2-3 bars in our house, and sometimes 4 (the max). When we called AT&T, they were much more helpful, and patched us over to an Apple engineer who seemed to diagnose the issue right away. #CheckTheESim