Has anyone else encountered this issue? If so, could you please share some insights?
Yes, that’s what @NotMyFault means. The Jenkins plugin manager recommends that administrators remove deprecated plugins because the plugin is either obsolete, no longer being developed, or may no longer work. In this case, the plugins are obsolete and no longer being developed.
As a safety measure, the Jenkins plugin manager won’t allow the administrator to remove a plugin that is a declared dependency of another installed plugin. Both those plugins are unlikely to be a declared dependency of an installed plugin.
The JQuery UI plugin 1.0.2 (last released 12 years ago) has only two plugins that depend on it. Both those plugins were last released 10 years ago. If either of those plugins are installed, then the plugin manager won’t allow JQuery UI plugin 1.0.2 to be removed.