"Sender address rejected: Null sender not allowed here" when forwarding e-mail sent from an gmail address

This is all caused by your mail server's interaction with your ISP's mail server, being rejected by that server.

Let's look at what is going on.

Dec 27 15:10:40 bowser sm-mta[76444]: 0BREAbT3071556: to=<[email protected]>, delay=00:00:02, xdelay=00:00:01, mailer=relay, pri=32614, relay=my.isp.relay.host.example. [IPv4-address], dsn=5.7.1, reply=554 5.7.1 <[email protected]>: Sender address rejected: Access denied, stat=Service unavailable

First your server tries to relay your email and gets rejected because they don't like the envelope sender.

Dec 27 15:10:40 bowser sm-mta[76444]: 0BREAeT2076444: to=<[email protected]>, delay=00:00:00, xdelay=00:00:00, mailer=relay, pri=34394, relay=my.isp.relay.host.example. [IPv4-address], dsn=5.7.1, reply=554 5.7.1 <>: Sender address rejected: Null sender not allowed here, stat=Service unavailable

Next, your server generates a bounce email and tries to send that bounce message out via the ISP's email server. Bounce messages have an empty envelope sender.

It's not clear why you're trying to send this email via your ISP's server, as (1) you say it works when you send directly, and (2) your business class Internet service should permit you to send mail directly to anywhere (if it doesn't, start yelling at your ISP until they fix it).