I have a valid family ESTA but have changed my passport. Do I need to renew the whole family ESTA or just do a fresh one for me and use the existing one for the other family members?
There is no such thing as a "family ESTA". The US government provides the facility to submit a group of applications at the same time, but this can be used by anyone, and there is no obligation that you are related, nor that you actually travel together.
The validity of your ESTA has no bearing on the rest of your family. There is no need for them to reapply for an ESTA when you do.