You already have a public IP address the only difference is if you have a rotating IP address which is orthogonal to IPv6.
The only difference is most ISPs rotate IPv4 but not IPv6.
Heck IPv6 allows more rotation of IPs since it has larger address spaces.
IPv6 can "leak" MAC addresses of connected devices "behind the firewall" if you don't have the privacy extensions / random addresses in use.
There are a number of footguns for privacy with IPv6 that you need to know enough to avoid.