You should take into account that (besides survivorship bias), "Ancient Greeks" you know of are all part of the aristocracy: that means good food, no hard labor, and access to whatever health care was available at the time.

Isn't the idea that he average life expectancy in antiquity is 40 ish years more to do with the high infant mortality rate than anything else?

Doesn't this mean that modern medicine is pretty horrible though, apart from infant care? With all our know-how, theories, experience, tools, drugs, scanners, etc - we still basically aren't much better than ancient Greece?

Alternatively, it could mean our way of life is terrible and our medical knowledge is the only thing keeping us ahead.

Maybe, but if I didn't know we have similar life spans I would've guessed that modern life is far safer and healthier than ancient life. Some examples - better nutrition as evidenced by height and diet diversity, not drinking dirty water or eating dirty food, temperature controls, modern policing, not regularly exposed to dangerous animals or conditions, etc.

That's mostly hygiene. Bad hygiene is why cities are often associated with disease-- cities are often full of unhygienic practices that allow bacteria and virii to fester. They still didn't understand seizures, or cancer-- ie they were good at one dimension among many that exist in illnesses.

In Ancient Greece one of my favorite little tales is a toilet one. Toilet paper, of course, did not exist. And so the Greeks used sponges, often on a short stick. And these sponges would be cleaned by swirling them about in as bit of water, or for the fancy toilets - a bit of vinegar. They had communal butt brushes in other words.

And there are many other issues of similar effect. Many of the hygienic practices that we now generally believe are intuitive, were anything but. For instance the idea that doctors should wash their hands before examining patients or even doing surgery was simply unknown all the way up until the 19th century [1]. Incidentally, while a basic germ theory was proposed in the 16th century, it wasn't until the 19th that it would come to be accepted as valid.

[1] - https://www.history.com/news/hand-washing-disease-infection