From Anacanda-Navigator app version 2.6.2 under macOS Sonoma 14.6.1, I click the Connect button then click Sign In for Anaconda Cloud. That opens a page in Safari (17.6), namely:
(possibly sensitive part of that URL elided). But the page is just blank!
There is a known issue with Safari at the moment that our team is working through. In the meantime, you could use another browser (I recommend using Chrome). Sorry for the current inconvenience.