Leaning in and turning in are two different things and are very different in effect.
Leaning the bike produces camber thrust and turns independent of steering angle
turning the bars to the left moves the centre of gravity to the right and gyroscopic precession tips the bike to the right
speed has a huge affect on this camber thrust and gyroscopic precession and tiller action / steering angle are all effects that are real
if we had to think how it works we would all fall off our bikes – even Jedi
A switchback goes up and down in a straight line in English
Its an awfully complex thing to untangle in words get someone who really knows to watch you and they will see what is happening n a tenth of a second