I agree, though chattel slavery typically implies the slavery of offspring. You can still have institutionalized slavery without that, like the Romans and a lot of other cultures throughout history. Slaves could be set free, could have semi-decent standards of living, while still being dehumanized. Or they could be treated brutally and enslaved for generations. The term seems to fit here in the broadest sense of the word.

"Slavery" etymology takes its roots with the "Slavs" people, who were, well, enslaved in medieval times. The term has been commonly accepted to describe various similar patterns before and after those times.

I agree that yesterday or today slavery is just slavery, whatever subtile differences there might be.

Not all slavery is chattel slavery.

A good example of another type being forced labor via debt bondage.