Regarding the messages.

DEBUG: .../IO/Socket/SSL.pm:525 refers to the 525th line of the installed SSL.pm module, as the place of message origin.

250-STARTTLS in the EHLO response indicates the availability (server willingness). Line with 530 is the actual error.

Email::Send::SMTP::Gmail has Net::SSLeay among its dependencies. Net::SSLeay provides the actual glue to openssl library.

See if you can increase the debugging level by including

$Net::SSLeay::trace = 2;

in your program. The detailed handshake may bring you closer to the cause of the failure.