I have not done the SMTP debug yet but just from basic troubleshooting, I think I know what the problem is. My mail server is rejecting my web server from sending mail due to 'relay access denied':
root@www:# telnet mail.domain.tld 25
Trying 211.113.101.135...
Connected to mail.domain.tld.
Escape character is '^]'.
220 mail.domain.tld ESMTP Postfix
EHLO www.domain.tld
250-mail.domain.tld
250-PIPELINING
250-SIZE 20480000
250-VRFY
250-ETRN
250-STARTTLS
250-ENHANCEDSTATUSCODES
250-8BITMIME
250 DSN
MAIL FROM:carlos@domain.tld
250 2.1.0 Ok
RCPT TO:some.email@gmail.com
554 5.7.1 <some.email@gmail.com>: Relay access denied
quit
221 2.0.0 Bye
Now the above was my web server on the same network / same subnet trying to access my mail server.
mail - 192.168.1.200 / 211.113.101.135
www - 192.168.1.201 / 211.113.101.136
Above addresses are internal IP / external static IP.
However when I look in my mail server logs, I see:
Dec 17 14:27:45 mail dovecot: imap-login: Login: user=, method=PLAIN, rip=211.113.101.136, lip=192.168.0.200, mpid=8013, TLS
Dec 17 14:27:45 mail dovecot: imap(carlos): Disconnected: Logged out bytes=94/885