To make a long story short, is there an easy way (module or whatever) to easily extract subroutines from a Perl script using a Perl script?
To make a long answer short, no. Perl is a context-sensitive language which defies any attempt to write a simple parser. You'll either have to settle for something simple that doesn't handle edge cases or something complex that does.
As an aside, you might be intersted in this take on "only perl can parse Perl": Chasing Shadows
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