New installation Zimbra mails end up in Spam folder of Gmail and Yahoo

Modern major mail services score spamminess based on multiple reputation factors, if available.

If the only factor is your IP and you don't mail often, this might be "the reputation of the /24 my IP is in". If you mail a lot, you might get your own reputation.

The easiest way to get reputation which "drowns out" the IP reputation of your netblock is to set up DKIM. Send your mails signed. This will establish a per-domain reputation, instead of per-IP reputation, and provides more signal to the automated scoring systems.

The more you work to help the recipients of your email figure out who you are and how trustworthy you are, the more signals they have to work with and the better a job the automated systems can do in deciding that you're legitimate, unlike whoever else bought a virtual machine in the same netblock, pumped out spam and then left, bills to hosting service unpaid and everyone else's reputation tarnished.

[some years later]: I wrote a blog post a couple of years back, walking through a lot of the steps needed to be able to more reliably send to large mail providers: https://bridge.grumpy-troll.org/2020/07/small-mailserver-bcp/

I don't see any public IP addresses in your header... Did you send one to yourself? If so, that won't work. We need to see the headers after it arrives at Yahoo or Hotmail.
One thing I do see is that your mail server thinks you are on a SORBS Blacklist. If you are, then Yahoo and Hotmail will most certainly tag your emails as spam...

Update: You are on 5 blacklists according to: MXTOOLBOX. This is for sure the reason you are getting put in the junk folder at Yahoo and Hotmail.