There was no related change in the image - deploying a previous image had the same behavior.
My static files started taking 1min to transfer. This caused my app to also hit hard limits on connections due to all the pending static file requests.
I fixed this by removing the [[statics]] sections from my fly.toml and magically everything started working.
All the while status.fly.io says All systems operational. I question that page. Please keep it updated.