jEdit should search in a subfolder "jre" where a jlink'ed JDK 11 would do the trick. E.g. Launch4j offers that explicitly. Best of all would be if jEdit would have something like config.ini in the folder where a jre can be configured relatively to the executable. Eclipse does it that way. Moving forward to JDK 11 is a good thing for sure. It gives jEdit a future. But you should rethink to deliver the installer with a specific jre which comes along. It's not that big if you strip it down to the needed...
plantuml syntax coloring
PlantUML syntax for jEdit