IPv6 doesn't have NAT, it has different addresses for global and local scopes, but your OS never translates between these addresses and it doesn't need to keep a table of translations & connections, as you'd have with IPv4 and NAT.
This is widely believed, but it's false. There is nothing whatsoever stopping you doing NAT with IPv6, even though you probably don't need to.
In the early to mid 90's, nobody did NAT with IPv4 either.
Your client machines don't know what is going on at the border, so they can't "choose" a route out unless you turn the lot into routers and use OSPF or something internally.
So NPT. Your router sends flows out over links and rewrites the prefix accordingly for that link. Its a bit horrible and I've decided not to bother yet.
And surely you can do NAT with IPv6, Google for NAT66, but your average Linux box can do it. It's just almost never needed.