Geoserver is compatible with Java-11. However, Geonetwork is compatible with Java-8. Is there a set of versions for Java, Geoserver, and Geonetwork, compatible with each other?
You could choose to run the maintenance branch: GeoServer 2.22.4 is still compatible with Java 8 at this time; however it will reach end-of-life in September:
Next week is the Bolsena Code Sprint, Java 11 compatibility is one of the topics you could put to the GeoNetwork Project Steering Committee for their attention.
Of course if you are in position to help out with development or testing it is appreciated. If you are not in position to help out directly there still may be an opportunity to look at commercial support or sponsorship as appropriate.
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Jody Garnett