Bike starts and then immediately dies

You didn't mention the choke. Does it still drop if you start with the choke out; let it warm up for a few minutes and push back in? Maybe it just doesn't like cold starts. Also I'd consider enriching your mixture; I'm no sport bike expert but 1,200-1,300k could be slightly low idle for a 636. Try 1,500. A combo of choke and mixture may do it.
pikashow.fyi
ppssppgold.one

sounds like it might also be a carb problem...when is the last time you cleaned them out? Will it continue to run if you hit the throttle?