Even their status page is down. But, prior to that their two primary APIs were down. I believe those are the two main relays that operate the network, so Blacksky is down as well. I'm not sure about Eurosky.

https://status.bsky.app/

Looks like some network activity is coming back online.

>From: Bluesky Server Status ‪@status.bsky.app‬

Update: We are starting to see some early recovery, but many users and services are still impacted.

https://bsky.app/profile/status.bsky.app/post/3mjm3qxzxeo2x