One interesting thing about the cat mummies here is that they'll provide additional datapoints on how well fed temple-sacrificial cats were and how they were killed. And perhaps at some point some ancient DNA can be sequenced? Which will give interesting data about how domesticated they were. Bradshaw in _Cat Sense_ argues that the core work of domesticating cats was accomplished by the Ancient Egyptians as a byproduct of their large-scale breeding, necessary for the raising the vast volumes of cats to be sacrificed as offerings.
The most common cats in ancient Egypt are still around today, https://en.wikipedia.org/wiki/African_wildcat and https://en.wikipedia.org/wiki/Jungle_cat
I know this does doesn't quite answer your "changed over time" question, but it is a data point.