First thing; sanity check: the orientation of the red wire and the leg from the inductor do not matter. They don’t even need to connect to the PCB, just each other. The location on the PCB is provided for tidiness and physical strength.
The circuit does not look familiar to me.
The markings on [what I assume is] the buck controller look exactly the way QX9920 is marked. I don’t know what the markings mean, but the numbers change - maybe it’s batch numbers? The pinout may not match, it’s very difficult to tell because many traces go under other components.
The unmarked chip is most likely just some crap “flashlight modes” chip. It’s not very important, assuming I am correct. If it’s a familiar model you might be able to short pins on it in order to change mode groups.
Do you have a multimeter? If so it would be a good thing to do to check voltage at all pins on the “LEDA” chip in both “High” and “Medium” modes. Check them against ground.