use is somewhat of an “overloaded” construct in Perl. It can be employed to reference an outside module (use foo;), or as a pragma to request certain compile-time behavior (use strict;).

I think that explanation confuses more than it enlightens. In both cases (pragma and module), use does the same thing:

BEGIN
{
    require 'Module.pm':
    'Module'->import;
};
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It always performs the require (modulo Perl's internal cache of what it's already loaded) and it always performs the import (modulo use Foo ();). use has no idea of whether what it's loading is a pragma. That part's up to the loaded thing's import() method.