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What you describe is what some call counter steering.
You’re certainly tenacious - an entire Wikipedia page telling you the definition, not including your definition, and telling you it’s how bicycle steering works doesn’t slow you down!
I think rather than arguing with me you should correct Wikipedia and see how far you get. You should also attend to https://en.wikipedia.org/wiki/Bicycle_and_motorcycle_dynamics, that weirdly doesn’t seem to mention your special facts on how bicycle steering works.
I have a feeling you’re mixing up the direction of the force you have to apply with the angle of the wheel. Also, countersteering is about how you change the radius of your turn, not about what angle you hold on a steady-state turn.
The effects of the round tire profile are a factor that alter the steering angle for a given turn - conceivably even against to the direction you turn, but as you can see from the Wikipedia page linked that’s not what the term means.
And ultimately, it’s the only way you initiate a turn, no matter how much many people disbelieve it. As the page says “While this appears to be a complex sequence of motions, it is performed by every child who rides a bicycle. The entire sequence goes largely unnoticed by most riders, which is why some assert that they do not do it.”