They can't log in to update the status page about facebook login because they use facebook login for auth on the status page!
Joking aside, I wouldn't be surprised if this was the case, because during their last major outage (something related to DNS iirc) they were having issues pushing fixes because they couldn't login because their DNS was down.
EDIT: seems like the status page was recently updated.
https://metastatus.com/facebook-login
Platform Status : No known issues Mar 5 2024 4:38 PM GMT+1
The service is up and running with no known issues.