In your top illustration they left out the V-Twin cruiser type bikes, that by design many will start dragging metal parts in around that 35* lean angle.
Well....that's one way to explain it. Or, simply, to turn left push the left bar forward, the bike leans left and turns left. To turn right push on the right bar forward, the bike leans right and turns right. Or, "push left turn left, push right turn right". Some folks will never understand the principle and will never care to, they just want to know what to do to get the results. A lot more folks appreciate a simple physics explanation then quickly forget and just keep the actions they need to do what they want. A very few need to know all the geometry and physics and fortunately for them there is a ton (maybe 2 tons) of information on the web written by accredited scholars with years of research and fancy diplomas who, will explain it in very complex and never ending numbers and angles. I know I have been down that rabbit hole a few times!!Then, the rider IMAGINES , or VISUALIZES,