TL;DR; This should be resolved now.
This was an issue with the SQL Server clusters that took us offline. Over the last couple of weeks, we have been upgrading the storage on quite a few of our SQL Servers. Last night, we did a failover of the main servers - the servers that run Stack Overflow, the SE Network, Jobs, and Chat - plus other things. While it took a little while for the failover to finish it appeared everything worked as expected.
Fast forward about 6 hours to this morning, I did the prepwork so we could upgrade the storage on the last couple of servers. Fast forward another hour and I shut the secondary SQL Server for Stack Overflow down. As soon as that happened, we noticed that exceptions were spiking and we were alerted that the network failing.
During the investigation and trying to bring the servers back online, we noticed that when the failover took place on the Stack Overflow cluster the quorum votes were not correct. The vote stayed on the secondary that I shutdown this morning, instead of being on the primary server in the cluster. Since the vote weight was wrong, we went offline.
After moving the vote to the primary server in the cluster, we came back online everywhere. It was an exciting morning all around.