Safari Browser on M2 MacBook Air won't let me sign in.

We understand the inconvenience of not being able to sign into your account on the Safari browser, and we are here to assist, @ElChromeDome.

Are you able to connect to other sites other than the AT&T website?
Is this happening on multiple devices or just the Macbook Air?

We recommend the following:

• Try accessing the site using another browser. 
• Clear your cache and cookies. This will help refresh your browser by clearing the browsing data, which includes your cookies, cache, and history.
• In case you are connected to mobile data, please disable the data so your device is able to pick the Wi-Fi connection rather than defaulting to your data. 
• If all sites are not loading, restart your gateway. A gateway restart will clear any errors that might be impacting your connection.
• Double-check the internet speeds, to make sure your AT&T Wi-Fi gateway is getting enough upload and download speeds. 

Let us know if the above steps help or if you would like additional assistance. If all sites are down and you have tried all these steps with no resolution, we can meet in a Direct Message so we can review your account and perform some troubleshooting steps.

Amon, AT&T Community Specialist.

No problems with either Safari or Firefox on my M1 MacBook Pro. As suggested try clearing the cache or see if you can login with Firefox. I'm assuming you have no other issues with apps connecting (like Mail, etc).

Turn off private relay. That’s what was causing mine to not work with safari 

Isn't Private Relay an iCloud+ subscription feature?

Yes it is. I was having the same issue as OP. I turned off private relay and I was able to log in. Could be a VPN as well. 
Same on my MacBook Pro M2 as well