When doing this sort of investigation, I find the core utility corelist to be very useful. This has a number of options; here's a selection of examples:

$ corelist File::Copy

Data for 2022-05-27
File::Copy was first released with perl 5.002

$ corelist -v 5.034000 File::Copy
File::Copy 2.35

$ corelist -a File::Copy

Data for 2022-05-27
File::Copy was first released with perl 5.002
  5.002      1.5
  ...
  v5.34.0    2.35
  ...
  v5.36.0    2.39
[download]

Note that some modules have been added then removed from core:

$ corelist CGI

Data for 2022-05-27
CGI was first released with perl 5.004, deprecated (will be CPAN-only)
+ in v5.19.7 and removed from v5.21.0
[download]

If it's important to you, perlhist gives the date of Perl releases.

Modules which are core, but do not have a separate CPAN version, will show perl-<version> as the distribution when you search for them using MetaCPAN; for instance, "MetaCPAN: File::Copy" gives:

Ricardo SIGNES / perl-5.36.0 / File::Copy

On the left-hand panel, under TOOLS, the Download link points to the tarball: 'https://cpan.metacpan.org/authors/id/R/RJ/RJBS/perl-5.36.0.tar.gz'. You can't install this module separately from CPAN.

Modules which are core, but also have a separate CPAN version, show a distribution which is not perl-<version>; it may reflect the module name, e.g. Some-Module-<version>, or it may be part of a bundle of modules under a different name, e.g. Various-Modules-<version>. For instance:

$ corelist List::Util

Data for 2022-05-27
List::Util was first released with perl v5.7.3

$ corelist -a List::Util | tail -2
  v5.36.0    1.62
[download]

From "MetaCPAN: List::Util":

Paul Evans / Scalar-List-Utils-1.63 / List::Util

The distribution name is a link. Follow this to get additional information, including a list of bundled modules.

Also under TOOLS (left-hand panel) there's a "Jump to version" dropdown list: possibly useful if you want to install an older version from CPAN.