Do I still need a seal coat over painted, stained, or polyurethaned wood?

Yes. Paint, stain and polyurethane are not substitutes for the epoxy seal coat. Whatever finish is on the wood, you still brush on a seal coat of UltraClear Bar & Table Top Epoxy, then pour the flood coat 4 to 6 hours later. Tinting the epoxy opaque doesn't let you skip it either; the wood still pushes air bubbles into the pour.

What changes is how you prepare the existing finish.

Paint: latex and water-based paints are best and dry fast; the epoxy can go over them after about 24 hours. Oil-based paint takes a long time to fully dry, so seal it with 3 coats of oil-based polyurethane first or the epoxy may not bond and can peel off months later.

Stain: water-based and latex stains are fine once dry, typically 24 hours. Oil-based stain needs 3 coats of oil-based polyurethane, dried at least 24 hours, before the epoxy goes on.

Polyurethane: the epoxy only works over oil-based poly. Over water-based poly, apply 3 coats of oil-based poly, let it dry at least 24 hours, then seal coat and flood coat as normal.

Oil finishes such as tung oil: even after sanding, the oil can cause adhesion problems unless the wood is stripped back to raw. The safe route is 3 coats of oil-based polyurethane, 24 hours to dry, then the epoxy.

Note that all epoxy has a slight amber tone that only shows over something completely white; oil-based polyurethane has the same effect.