As for how "property" is defined, in your bible it is pretty clear: slaves are the property of their owners, to the point where they can be traded like common goods and be inherited by off spring. They are property in every sense of the word.
You are throwing the word
property like it must have the same contextual meaning as it is to you today. That's simply not the case.
Slaves were "property" as much as a modern worker paying off a debt, or a prisoner working for pennies on the dollar are a "property", or a soldier or athlete signing a contract becomes a "property". The correct economic definition is an
"worker asset". They were not entitled to "owning a person". Owners were entitled to
their labor as a
contractual debt payment means for a certain period of time.
The masters were responsible for slaves. Slaves were their responsibility. In context of children of slaves, they were responsible for them, because contextually they would be safer in that environment than migrating with no home or means of supporting themselves. Same goes for women.
In fact, your modern context of slavery of "kidnapping for ownership" was a death-punishable offense.
“Anyone who kidnaps someone is to be put to death, whether the victim has been sold or is still in the kidnapper’s possession." Ex 16.
If slaves were property, then the following wouldn't make sense in context of property laws. The stolen property was to be returned:
If a slave has taken refuge with you, do not hand them over to their master. Let them live among you wherever they like and in whatever town they choose. Do not oppress them.
Slavery was a primarily economic mechanism for paying off debts, serving prison sentence, dealing with surrendered enemy during war, or making sure that women and children had means of surviving. All of that was contractual, and was governed by common law.
Slavery was a contractual agreement, just like marriage was a contractual agreement. You could escape it. You could leave.
You could face consequences, as you would be leaving with nothing, and it would usually mean death. Or you could find community that could adopt you. Or it could be that the debt-owner would seek you out and seek penalty for breaking contract.
Either way, it's not the "ownership" that you are painting it to be.