Here's some troubleshooting tips. You'll need to make a few adjustments for your MSWin vs. my Cygwin: double quotes around perl commands springs to mind; there may be others.

If cpan is telling you "LWP::Protocol::https is up to date", but perl is telling you "LWP::Protocol::https not installed", that generally suggests you're running different versions. They should be in the same directory:

$ which perl
/home/ken/perl5/perlbrew/perls/perl-5.36.0/bin/perl

$ which cpan
/home/ken/perl5/perlbrew/perls/perl-5.36.0/bin/cpan
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Check what's in @INC:

$ perl -E 'say for @INC'
/home/ken/perl5/perlbrew/perls/perl-5.36.0/lib/site_perl/5.36.0/cygwin
+-thread-multi
/home/ken/perl5/perlbrew/perls/perl-5.36.0/lib/site_perl/5.36.0
/home/ken/perl5/perlbrew/perls/perl-5.36.0/lib/5.36.0/cygwin-thread-mu
+lti
/home/ken/perl5/perlbrew/perls/perl-5.36.0/lib/5.36.0
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perl -V will give you that information and a lot more. There could be something useful in that output.

Try to load just the module:

$ perl -e 'use LWP::Protocol::https'
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That will just return (no output) on success or you might get "Can't locate LWP/Protocol/https.pm in @INC ...".

If that was successful, get more information:

$ perl -E 'use LWP::Protocol::https; say $LWP::Protocol::https::VERSIO
+N; say $INC{"LWP/Protocol/https.pm"}'
6.10
/home/ken/perl5/perlbrew/perls/perl-5.36.0/lib/site_perl/5.36.0/LWP/Pr
+otocol/https.pm
[download]

Note that last line of output should match a directory in @INC obtained earlier. In my case:

/home/ken/perl5/perlbrew/perls/perl-5.36.0/lib/site_perl/5.36.0
[download]

See how you go with those. A solution might present itself. If still stumped, post all output from those commands and we can look into it further.