I renamed a feature class in ArcPro using catalog, which caused disconnected layers in a map. Previously, in Pro, renaming an item in a file geodatabase would cascade through the .aprx with no disconnected layers. What changed?
I hope you are doing well today. Regarding your issue, I just tried this out myself at Pro 2.6.2 with sample data stored in a local fgdb, and didn't experience the issue described. Once renaming the feature class, I went to the layer properties in the content pane > Source tab, and it looks like the updated name carried over.
When you say the layer is disconnected, does it gray out, get a red exclamation point, etc.? If you open a new test project, insert a sample feature class and change the name, does the issue persist?