Consider using Crypt::PK::RSA which supports import of encrypted RSA keys in PEM format.

use Crypt::PK::RSA;
 
my $pkrsa = Crypt::PK::RSA->new("priv.pem", $password);
my $data = 'any data you want to sign';
my $signature = $pkrsa->sign_message($data, "SHA256", "v1.5");
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It seems to interoperate well with openssl.