Unfortunately, you updated improperly. The update technique described at that site is ill-advised (though very creative, creative in a way that I would never have considered). The update technique described on that page modifies the jenkins.war inside the Docker container image by downloading a new jenkins.war inside the image.
Files packaged into Docker containers are generally considered to be immutable. In that update technique, it is modifying a file that should be immutable.
Because you changed the jenkins.war file inside an existing image, you did not change any of the other components that are part of an updated Jenkins Docker image. Your docker image now contains a newer Jenkins war file with the same Java version as it had before and the same other files as it had before.
If you instead define a Dockerfile that uses
FROM jenkins/jenkins:2.303.1, you will have the Jenkins updated Docker image with an updated Java version (and Java 11), updated jenkins.war file, and updated operating system files that may be used by Jenkins.