Can't thread crank puller
Try removing the black finish with a small wire brush. It may be anondized and difficult to remove. Regrease both sets of threads. I always start by giving the tool a quarter turn or so to the left before proceeding to the right. Seems to line the threads up and helps prevent cross threading.
In this area of the bike (cranks, bottom bracket) it's best practice to at first hand thread the tool, bottom bracket cup, crank fixing bolt, etc as a measure to prevent cross threading.  Regarding the crank puller: the outer nut needs to be threaded fully into the crank arm good and tight before you attempt to wind in  the center bolt that pulls the crank arm. You risk damaging the crank arm threads if the tool isn't fully engaged with the crank arm. Thus &quot;hand tight&quot; as you described would be risky.  A common error related to this is not having that center bolt of the crank puller backed out enough and so it bottoms out on the square taper before the outer nut is fully engaged in the crank arm.  Same deal: the crank arm threads strip or become damaged making subsequent removal difficult or impossible without ruining the crank arm