Updating the question with an answer - Certiport is sending emails to people encouraging them to use Credly, but according to the answer below, Microsoft doesn't use Credly anymore.
After passing an exam, I received an email from Certiport congratulating me on earning a certification, and encouraging me to visit Credly to claim my badge. I had no account at Credly, so I created one. It's been a couple of weeks now and no badge has magically appeared in my profile. The email sent me to this link docs.microsoft.com/en-us/learn/certifications/badges which actually had a page worth of information on the day I opened the email but now forwards me to a bloated page about Credentials Overview. https://learn.microsoft.com/en-us/credentials/support/cred-overview
Could not find anything in there about Credly using the left-hand nav. Found this page by searching ... for credly https://learn.microsoft.com/en-us/credentials/certifications/posts/how-to-claim-your-digital-badge-and-why
I tried to get support from Credly and it said that I needed to contact the issuer of the badge. Credentials support page sent me to this forum.
In my learn profile, I am seeing my old certifications from years ago but nothing from the latest exam passed. I do understand that some certifications require passing more than one exam, but all the language seems to indicate to me that I can at least claim to be an "expert" in the one that I have passed and I should be able to get a badge from Credly. I would also expect that it should be showing in my learn profile.