Those look like 'conventional' woodscrews, single thread, tapered core.
You may find life easier with a more recent twin start thread screw with a parallel core. Drill the clearance hole in the drawer front for the thread/shank, whichever is largest, all the way through. That way you don't end up with a turn, or two, of the screw trapped between the knob and the drawer front. Make shure that the pilot hole in the knob is as near to the core diameter of the screw as possible, without being larger. That recipe normally works for me.
It is important that the pilot hole, in the knob, is square to the back face of the knob. Check by putting a drill of the correct diameter in the hole and gauging by eye. You will see if it is a long way out by spinning the drill between your fingers. If the knob appears to wobble, the hole is off square.
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