I just recently got my first bike and like you, it's not enough for me to know that it works...i want to understand how and why things work so i can consciously apply them
My bike is nothing like the one you drive, it was a bargain sale from a friend of mine. It's a Honda FMX 650 single cylinder, styled like a supermotard but way more underpowered that most supermotards, at 37-40 odd horsepower ( stock is 35, but i got it with after-market remus exhausts on, which are still street legal while upping the performance a bit). If i modify it a bit i can probably get it to 45-50 hp and still be street legal (i got the exhausts, i only need a high flow air filter and readjusting the carbs to avoid running lean after making it "breathe" better), which is plenty for a novice rider like me on a bike that has a gross fueled weight of only 163kgr.
Nevertheless, i went through a similar thing as you. I've had a license for a few years but not a bike, the opportunity presented itself and then i started reading up on everything i could find and watching youtube tutorials on riding techniques and safety tips.
Where am i getting at? I'm really surprised you've been driving for quite a few years and hadn't heard of countersteering before, especially since in many of the EU countries training for a license is much more extensive. Truth be told, they didn't teach it to me in driving school either, but i was reading up on my own and found out about it when i started taking driving lessons.
In short, countersteering is what saves rider lives. Most accidents happen (like 90% of them, according to EU studies) in residential areas because a car will not see you, cut you off and you lack the space to brake in time to avoid a crash.
If you can countersteer, you can start braking and when you realize you can't stop in time, you'll be in a sufficiently low speed to simply swerve by the obstacle.
If you couple that with our natural tendency for target fixation (the old "the bike goes where you look" saying) and set yourself up to consciously practice it every day, you are dramatically improving your accident avoidance skills: look at the opening between the obstacles and push the handlebars to go there.
I'm not trying to be pompous and "school" someone who's been riding far longer than i have and currently rides on the race track with much faster bikes. I'm just glad you discovered this life-saving technique and i want to emphasize that it's perfectly fine for everyday street use, not just for the track. Most bikes start to get effective at countersteering around the 20-30km/h mark, depending on their chassis and geometry. Even when below that speed however, you can initiate a turn by a split-second momentary countersteer, then turn the wheel into the turn to keep the bike from falling over (instead of just centering it when you lean the bike over by countersteering at higher speeds).
Finally, it's not only effective, it's also faster than leaning your entire body and works both ways: push into the turn to lean into the turn, push outside the turn to get the bike level again.
The only thing to remember is that the faster you go, the more you need to push on the handlebars and vice versa. So, if you come from the track and try to apply it on an everyday ride, you will need much less force and a way more subtle movement of the handles. Get some half-empty plastic water bottles, go out on an empty parking lot, do a cone weave around the bottles for half an hour or so and you'll be good to go in no time. Ride safe and have fun