Minwax makes 2 different Wood Fillers and one Wood Putty. If you used the kind that is kind of like a big wax crayon, there is not much that you can do other than refinish if you really want to hide the nail head marks. This product works great on things like covering the nail heads in clear finished moldings but not so well for furniture like applications.
For furniture type use, you can use Minwax High Performance Wood Filler to fill the holes before the staining and varnish or poly. This is an epoxy type product and is supposed to take stain but doesn’t. Stain will not hurt it and you can blend the filler with the Minwax marker type blending products (like liquid paint sticks, not wax type) or equal or with tone sprays. Then the sanded, hard filler will blend under the poly or varnish nicely if you picked the right colors.
Of course, there was a lot simpler answer and that is to put cleats on the cabinetry under the bar top and run screws up from under the top, being sure that the screws are not so long that they go through the top surface.
Just putting a tone spray and more polyurethane over the current filler will not work for long because the wax will not let the poly maintain a bond. Poly will not hold for long where any wax remains.
Henry in MI