How can one identify the absolute safest car in practice rather than theory?

Another thing to consider is to what extent each manufacturer hyper-optimizes to pass safety tests (vs actually focusing on safety). I’m having trouble finding a good source for this, but I’ve heard that Volvo has a reputation for doing internal safety testing that goes beyond what NHTSA tests (which would make them safer than safety rankings indicate).

For example, they introduced their “Side Impact Production System” in 1991 (https://www.volvocars.com/us/v/car-safety/safety-heritage) and NHTSA started testing for side crash production in 1996 (https://www.nhtsa.gov/ratings).

I don’t know to what extent they (still) do this but it’s something to consider in any metrics.

One factor that I don't think is included in the official data is car color. As far as I remember cars with colors that make them more visible are more seldom involved in accidents.

Quick Googling finds https://www.citywidelaw.com/los-angeles-car-accident-attorney/car-color-and-crash-risk/ :

At least one study found that you’re 47 percent more likely to be in a crash if you drive a black vehicle. Other studies also find that black is the most dangerous color, but offer a more reserved projection. Those studies find that driving a black car increases the risk of a crash by anywhere between 10 and 20 percent.

According to that page Gold/Orange/Yellow/White are the safest colors.

Start with the basics. Make sure each passenger is buckled in, and that they have the seat angle and headrest etc at an appropriate position. I actually have some automation whenever I enter my car (Tasker yay!) that do things I tend to forget to do, and opens up a talking checklist that I go through before starting the car or after parking. (I can make a post if there's interest.)

I bought a dashcam to help improve my driving (plans before every drive, then a critical review of drives). I also found good channels for advanced driving (e.g., Advanced Driving and Reg Local, from the UK) and more basic stuff (Conquer Driving, Advanced Driving again, Conduite Facile) to refresh.

In addition, I recommend cars with active safety technology. Even something like Adaptive Cruise Control, which keeps a safe distance from the car in front of you, reduces your cognitive overhead by quite a bit, and allows you to monitor the situation around you better (far, near, behind, etc). Add to that automatic braking, blind spot monitoring, alerts when there's cross traffic while reversing, lane keeping, 360° cameras around the car etc, and you've already prevented many of the crashes you might have gotten yourself into.

And finally, you'll want the actual protection in case of a crash. Find a bunch of safety tests, and find the ones with good safety ratings in multiple markets. Look at pictures of crashes. The more the car is shredded, and the more the passenger compartment is intact, the more likely you are to escape without a serious injury.

ETA: In terms of companies which I think are doing well with safety consiousness, I like Toyota (post 2018-ish) a lot, since they're providing advanced safety features even at the most basic trims. Also, consider using OpenPilot (CommaAI) instead of stock, because it tends to work better.

What else should I consider, and what other important factors am I not thinking of if my end goal is finding cars that are really a cut above the rest in terms of safety?

Are you thinking about your own skill at driving? Maybe you are, and left it out because that isn't the question you wanted to ask here, but it is something to think about. For all I know, you might have years of experience driving emergency vehicles with sirens through traffic at twice the speed limit without dying, but otherwise, some sort of advanced driver training might be something to look into.

Another thing to consider is what colour it should be. Anecdote: a friend of mine once went off a country road and violently bumped to a stop in a field. She was injured enough that she couldn't get out of her car. Fortunately, another driver came along, saw, and stopped to help, but she realised that because her car was dark-coloured, if this had happened at night she would have been invisible. Her next car was bright yellow.

I read a pdf some time ago (link lost) where was listed number of deaths for different types of cars. I remember that Kia Rio has 1 death for every 10 mln km, Toyota Prius - 1 for 1 billion and Dodge Caravan had no deaths.  However, later I found similar statistic and Prius had more accidents.