Something went wrong... Let's try this again
Since I wasn't able to find an easy answer to my problem and solved it on my own, I'm writing an answer here.
I went to register a new TV with HBOMax and immediately when I selected DirecTV or ATT as my provider, I would get an ATT-based error page saying "Something went wrong... Let's try this again." I cleared all my ATT cookies and it persisted. It happened even if I went to login to my ATT account directly.
I finally went to the MyATT app on my phone and it said "you haven't logged in for a while, let's verify your account" and it did the two-factor authentication by sending a code to my phone. After that, it showed me my account. And from there, everything else worked.
I don't know why it couldn't say the same thing on the web login. Not everyone uses apps. But it didn't even seem to get to the login credentials before it gave the error. I saw others post with the same error, saying they tried multiple browsers and everything. Clearly something needs to be fixed. But for now, it's a workaround.