I upgraded Oracle SQL Developer from 188.8.131.52 to 184.108.40.206, just for the heck of it. Unfortunately, all my saved connections had disappeared! After a text search I found the connections are stored in a file called IDEConnections.xml under the folder sqldeveloper\jdev\system\oracle.onlinedb.220.127.116.11.25. I copied this across to a new folder that had been created (oracle.onlinedb.18.104.22.168.36) and bingo they’re back again.
Bonus – now I know what file to back up if I want to restore my connections later on.