One of the issues you're going to have here is that an Active Directory zone is much more than just a normal zone file like you might expect with
bind. I mean, yes, it is a normal zone, but it also has integrated permissions which can't readily be backed up in a plain-text format.
(I assume you're after something in plain text due to the mention of git, and I'm guessing you want to diff the AD zone at different times)
But if you're dead set on doing this, the way to export your zone file is using
Export-DnsServerZone -Name ad.example.com -FileName ad.example.com.zone
Now, the documentation says you can specify a file path for
-FileName, but in my testing I actually wasn't able to do this. So that means this file is going to end up in
%WinDir%\System32\dns. You'll want to grab it from there and move it to your git repo and commit it.
Getting the zone file back in when you want to restore it however, isn't quite the same. There does not seem to be a nice powershell wrapper for this (probably because it's not something Microsoft want you doing with an integrated AD zone):
dnscmd /ZoneAdd ad.example.com /Primary /File ad.example.com.zone /load
Note that in doing this restore, you'll lose all permissions in the zone - but you will have your raw data, and you will be able to diff it in git.