Hey @MBender!
I connected the dots with an internal report from one of my Sales Engineer colleagues about this topic (so you can be sure your feedback has made it internally).
For other interested users (and to close the thread here): even minor changes in the JDBC URL that end up pointing to the exact same Database can cause a Server ID refresh – such as changing a JDBC URL in the format sqlserver://my.sql.server.local\\myinstance to sqlserver://my.sql.server.local;instanceName=myinstance