The issue started when I installed 26.08beta2 and persists after updating to the 26.08 stable release. To be able to update, I downloaded the install package from the GitHub release.
When I choose Tools->Check for Updates, I get an error message as below:
I also get “No updates available” with 26.08 on Mac. I use the default AnkiWeb server for syncing. I upgraded from 26.08beta2 to 26.08 via downloading and installing the .dmg file.
I reconfirm that “Check for Updates” still works for me:
With Version 26.08, the button correctly told me that there was an update available (and I installed it).
With Version 26.08.1, the button correctly told me “No updates available”.
OP: Perhaps there is some other sort of network-related problem that is being (incorrectly?) detected as an authentication issue? I suggest that you try some network-related troubleshooting activity to see if anything might possibly help. (Things like rebooting your computer, rebooting your router, trying a different network connection, disabling VPN, etc.)