Glad to hear that everything is working!
why not version 1.1 that is already available?
Plugins like this that have been split from core are explicitly bundled in the war file and listed in split-plugins.txt to enable the automatic installation. jdk-tool:1.0 had to be released before Jenkins 2.112 was released, so it depends on Jenkins 2.111. This means that there is a short time where a 2.111 user could install the plugin and have multiple instances of the same class on the classpath, which is bad, so once Jenkins 2.112 was released, I updated jdk-tool to depend on Jenkins 2.112 and released 1.1, so that 1.0 is no longer available from the update center for 2.111 users. There is no issue with bundling 1.0 or 1.1 in core, but if later releases of jdk-tool have significant changes, such as adding new dependencies, we would probably not want to make those versions be bundled in Jenkins core, so it's easiest to just leave 1.0 as the bundled version, and let people upgrade naturally through the update center.
Logging of Jenkins version downgrading is missing
I'm not sure offhand, but feel free to open a new issue requesting that logging be added (or a pull request to https://github.com/jenkinsci/jenkins, I think the right place would be this method).