Is File::Copy versioned separately from Perl itself? When I look at the CPAN page it looks like File::Copy shares the version number of the perl distribution it is included with

File::Copy is a core module which means that it is bundled and shipped with Perl. However, the core modules do not share their version numbers with the corresponding Perl version. The page you linked contains both the version number of Perl (in the crumbtrail at the top of the main div) and the different version number for File::Copy (at the top of the left margin). For core modules, Perl itself is the dist but each contained module is versioned separately.

So what's happening is that in perl 5.34.0 and earlier, a module that is included with Perl by default (File::Copy) is calling a module that is not (List::Util)? And then perl 5.36 removed this dependency?

Yes, with the exception that List::Util is a core module too. See modules for the full list of core modules.