IP address is one of many signals used to build a statistical profile.
It doesn't match you exactly to the other persons behind the same NAT, but it adds some information, raising the likelihood of ad coincidences a little. I have no idea how much. It's likely to depend on which IP address, and other tracking statistics.
If you have diligently blocked lots of tracking state, then IP address will be a relatively stronger signal, and this might (ironically) increase the likelihood of ad coincidences.
I think this has started happening to me lately! I use pihole with the default block lists as well (in the US), which of course doesn’t get everything, but generally works pretty well.
So today my wife and I were looking at dogs that need forever homes using her laptop
Later I got a dog food ad on my laptop that specifically mentioned shelter rescue pets. I haven’t used any of my devices or accounts for dog-related searches for at least two months.