This is one of those topics (as stated by a previous poster) that creates a lot of debate.
I think part of the problem is the actions taken (which can be very different) vs the physics and action of the bike (the same).
For example, when I took the MSF course 8 yrs ago, I had never really ridden a motorcycle, just a bicycle. In fact, they said you needed to know how to ride a bike to take the class. Though mostly, it was just the idea of balancing on two wheels.
In class, they would talk about pushing the bars left to go right and right to go left. At the slow speeds of the class, it was not something I could easily do and my brain was not getting it. It is of course counter intuitive.
So for example, if I am stopped on a road wanting to make a 90 degree left turn, I turn my handle bars and therefore my tire to the left (pull back on the left bar, push forward on the right) to start the bike pointing to the direction I want the bike to travel. There will be a leaning to the left as I negotiate the turn.
If I am riding down a straight road and I want to have some fun, I will start to slalom. I can do this 2 ways (probably more, but I primarily do it with these two methods). I most often will shift my weight back and forth (like swinging my hips). This will cause the bike to go side to side in a slalom motion, it can be tight or larger variations based on the degree of the hip swing. The other method is simply pushing the handlebars alternating fairly quickly.
Both will produce the same effect. Both seem very different actions. And actually the handlebar one does not feel as “safe” as the other due to my not engaging the whole body. It feels less fluid. Both probably actually are due to the same physical forces, but because I am actively doing different things with different parts of my body, it seems different to me.
Unless I am messing around, I do not actively think of pushing the handlebars to lean the bike. I may be doing that instinctively, but that is not what it going through my mind.
This is probably why there is such disagreement because when riding, we are doing things we are not thinking about.
I can say it does not take much of a push on the bars to create quite a lean (like don’t push much on a straight road), but it will come back to straight once pressure is removed.
I do love the feel of the bike when the whole body is engaged, it feels like you are a part of the bike and it is so fluid.
For the OP, quit translating and just go for a ride.