When I run my Java code from Eclipse ... "No X11 DISPLAY variable was set,". It is set, I can echo it. I can also run xeyes just fine. From my program I printed out all the environment variables.

you can download an installer that not only installs Java but also configures the PATH and JAVA_HOME environment variables. For example, with the Eclipse Temurin version of the JDK, setting JAVA_HOME ...

in collaboration with the Adoptium Working Group, today announced the latest release of Eclipse Temurin’s Java SE runtime. As organisations around the world reevaluate their approach to Java ...