The only difference is most ISPs rotate IPv4 but not IPv6.
Heck IPv6 allows more rotation of IPs since it has larger address spaces.
There are a number of footguns for privacy with IPv6 that you need to know enough to avoid.
On Linux, I think the defaults are left up to the distros so there is a chance of a privacy footgun there. Hopefully most distros follow the example set by Apple and Microsoft (a sentence I never thought I would write...)
No one is saying we should have activated IPv6 in its first iteration.