for my $to ( 'abc3\@gmail.com', 'abc2\@hotmail.com'){

When you use single quotes for literal strings, you don't want the backslash before @ (the backslash will remain part of the string).

my $from = "abc1\@gmail.com";   # double quotes
my $to   = 'abc3\@gmail.com';   # single quotes

print "from: $from";
print "to:   $to";

__END__
from: abc1@gmail.com
to:   abc3\@gmail.com           # !!
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Those addresses are Email::Send::Gmail-internally being extracted from the To/Cc/Bcc headers using Email::Address->parse(), which doesn't identify something like abc3\@gmail.com as a valid address, so the final list of recipients is empty — as the error message is trying to tell you.

#!/usr/bin/perl -l
use Email::Address;

@addresses = Email::Address->parse('abc3@gmail.com');
print "ok     : @addresses";

@addresses = Email::Address->parse('abc3\@gmail.com');
print "not ok : @addresses";

__END__
ok     : abc3@gmail.com
not ok :
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