I’m not sure I can even guess what the cause would be. It sounds like the error message is a WordPress error message. Perhaps somehow it is permissions related.
Why it would this affect only old vs new would be a mystery because from a Connections code perspective there is literally no distinction. In code there is no difference between and old and new category. I’m fairly certain the code Connections Categories has not really changed in regards to adding/editing since its release a decade ago.
The only thing I can think of is to make sure Connections is fully up to date along with any addons that may be installed.
Deactivate all plugins except Connections to see if the issue still persists.
You could try force resetting the core Connections role capabilities.
Not sure what else to suggest. Maybe it is somehow triggering a mod_security rule the web host has put in place???
Not sure if this helps, but I hope it does. Let me know.