The plugins { ... } block within pluginManagement { ... } never applies anything anywhere, nor adds anything to any classpath. It only defines default versions if those plugins are used somewhere in the same build without version, hence the apply false actually is useless.
Your build that build the convention plugin should have a dependency declared on the Android plugin instead. As your convention plugin is meant to apply the plugin, it is a dependency of that plugin.
If you really want to apply “whatever version is present”, you have to make one version present, which is what you did by adding it in the build script of the root project.
Btw. I’d like to recommend using a version catalog instead of script plugins for centralizing version declarations for several reasons. 