Connection Security: STARTTLS
You're fine. This says that Thunderbird must encrypt the communication with your server.
This line confirms that; see the starttls=1:
postfix/smtpd[103272]: disconnect from 1.2.3.4.subs.proxad.net[1.2.3.4] ehlo=2 starttls=1 auth=1 mail=1 rcpt=1 data=1 quit=1 commands=8
However, whether or not your connection to the Google inbound SMTP server is encrypted isn't stated in your log file.