What does a package manager "using" SemVer for apps look like in any meaningful way? The package manager never has to do any dependency resolution against the version number of an app, so, I would assume (and know, for the package managers I'm familiar with), the version number is just an arbitrary sequence of three numbers. A version number only becomes semantically relevant the machine when other things depend on (aka, use the public API of) it.
"package managers" as in apt, yum, npm, pip, etc ? They do not "use semver" for anything. Your versioning scheme is completely irrelevant to package managers. (as long as the format and separators match of course)