Thank you for updating the status here and very appreciated that.
We do see the same behavior for some of the customers that using AT&T that HTTP & HTTPS traffics no longer able to route (Not all websites).
From the analysis, we confirmed the HTTP/HTTPS packets is sent but not getting reply from remote servers. We also setup some test HTTP/HTTPS server to confirm whether the HTTP/HTTPS packets sent are reaching to the remote servers but the results is negative that the traffics sent is not even reach to the test servers. That shown that the issue is on the service provider level.
Do you tested the WAN health check HTTP method ? This should triggered the WAN health check failed and cellular WAN will be reset after failed sometimes.