..mmh what I'd try too will be setting $CGI::POST_MAX even before CGI::Carp or even in a BEGIN block just after use CGI

No need for any such extra typing , the documentation doesn't lie, and it is as simple as use CGI; $CGI::POST_MAX=...; ... and it should works 100% of the time.

you can also try to do the job on your own, like in A serious security problem with CGI.pm 3.01?:

No no no, that node is ~two decades old. If you're using CGI.pm that old upgrade.

Infact this seems very simliar to what happens in the CGI.pm code: You can insert temporarly some debug statements here in the module to dump what $content_length is at the moment.

A presumed beginner is supposed to debug CGI.pm? No way. Not funny. No.

See also Detecting when a $CGI::POST_MAX limit is exceeded and CGI.pm file upload freaking me out

Meh, long and exactly relevant .... shortcut https://metacpan.org/pod/CGI#Retrieving-cgi-errors