I'm a long time Jira Cloud user that wants to explore using Bitbucket for my company.
When I go to Bitbucket.org and try to log in, I'm taken to id.atlassian.com where I enter my Atlassian ID (Larry@HolyCowOnlineMarketing.com) and password. This appears to work, but when I get back to Bitbucket.org, I see endless "Sign in" popups whenever I try to do anything (even though it appears I'm logged in) and there's a "Something went wrong" message near the bottom of the screen:

If I log out and try to log in again, I appears to work, but I'm sent back to Bitbucket.org and NOT logged in. Then when I press the Log In button again, I see "We couldn't log you in":

I've tried this in the latest version of three different browsers (Chrome, Firefox and Safari) and in a Chrome Incognito (private) window. It behaves the same everywhere.
What am I doing wrong?