It is possible that paint might allow stains to reappear later. As an
insurance, you need a good primer coat. Kiltz usually works well, and
so too would shellac. As a matter of interest, not related to this, I
recall where I had used screws to place metal corner bead, painted it
after drywall compound, and later there appeared black spots where each
and every screw reacted with the dissimilar metal. I also had a door
that had been stained with a mahogany stain. The white paint
consistently had red bleed through. Later I learned to prime with
shellac. Shellac covers everything, including glass.
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Shel