Is att.net’s email service no longer compatible with Safari 13.1.2?

The following is from ATT support article https://www.att.com/support/article/email-support/KM1063685/

Supported browsers

You can use your AT&T email with the 2 most recent versions of Mozilla® Firefox®, Microsoft Edge, Google Chrome™, and Safari®. 

The information below may help:

The model year of an iMac is available at Apple menu > About This Mac.

A late-2009 through mid-2011 iMac can be upgraded to High Sierra 10.13.6 but no later version.

A late-2012 through late-2013 iMac can be upgraded to Catalina 10.15.7. See: How to get old versions of macOS - Apple Support

A mid-2014 or later can be upgraded to the current version of Big Sur. See: How to upgrade to macOS Big Sur - Apple Support

Note that if you have any non-Apple 32 bit apps, they will not run on Catalina or Big Sur and will need to be updated. See: 32-bit app compatibility with macOS High Sierra 10.13.4 and later - Apple Support

It's apparently not just Safari, but also Apple Mail, I suspect because they both share WebKit or other structural elements. At least that's my tentative theory. I have a client who has two very old AT&T free email accounts (actually yahoo) which worked ok until a few weeks ago. Suddenly they could not access either account on two iMacs (Mojave), two iPhones, and an iPad (iPhones and iPad are pretty new models running the current iOS). So that might let the version of Safari off the hook, because of the iPhones and iPad having the same problem.

After spending a couple hours on the phone with AT&T tech support we finally managed to reset a password which gave us access in Firefox but still not in Mail or Safari. Finally clients're incentivized to move to a different mail host, which I've been bugging them about for years.