I'm not a scientist. And, I admit I do not understand all I know about bikes or gyroscopes.
Yes, there is significant disagreement between scientists about precession from what I have read. My friend who is both an experienced motorcyclist and aeronautical engineer and physicist assures me it is only marginally relevant. (He also dismisses Bernoulli’s Principle as having little to do with flight.)
Also, motorcyclists disagree about the relevance of precession in motorcycle steering (often vehemently).
To my mind, precession provides a good description of what is happening while riding a motorcycle. That is a force operates 90 degrees in the direction of rotation. In the absence of an outside force another gyroscopic property controls the bike. That is rigidity in space. Of course, when this rigidity is lost, a gyroscope tumbles, i.e., the bike crashes.
But, with regard to the difference between the experiment with a bicycle wheel and a motorcycle in operation I think the higher speed and mass would make precession more forceful in a motorcycle.
It seems to me the experiment with a bicycle wheel using handle grips attached to the axle is only half the turn input. That replicates the push on the handlebar. That gets lean.
The other half is the resulting diagonal force applied by the road to the contact patch - that gets the turn.
The force seems to be there, however we may interpret it.
Just some thoughts.