For various cultures around the world, when did abortion services first become physically safe and reliable (at least for the women with sufficient knowledge and means to locate those services)?

There are instructions on how to terminate a pregnancy in the bible. Not sure how safe it is.

Definitely no sooner than the very late 1800s when Louis Pasteur’s germ theory became widely accepted. This was a very regional thing however, with many western health care providers still resisting the idea right up until WWI.

Even after it became widely accepted, it was still often done unsafely by amateurs until it became legalized in the respective nations. Anywhere it was illegal, it was common practice to resort to so-called “back alley abortions”, almost always done by midwives as a secret side gig with inadequate instruments, hygiene and near total lack of anesthesia.

I’m not sure when they became physically safe and reliable, but Roe vs Wade was passed because of how many women were dying from unsafe abortions. There were also specific “homes” where unwed mothers were sent to have their babies, and these children were given up for adoption (typically sold to rich families) and the money kept by the home with none given to the mother. Some of these homes were found to have killed numerous infants or adopted babies out without the mother’s permission. Butterbox Babies is the term used to refer to infants that died at the Ideal Maternity Home (operated from 1928 to 1947) and were buried in small wooden grocery boxes (usually used for dairy products).

Here is a gallery of unsafe abortion methods that have killed women and contributed to the passing of Roe vs Wade.

As soon as it became legal and done by doctors in a safe/sanitized and controlled environment.

IIRC the Romans had Silphium, which they used as kind of a morning after pill. It couldn’t be farmed and it was in such high demand that they harvested it to extinction. The heart symbol we use to mean love may be based off the shape of silphium seeds.