Can you use a water based stain over paint?

No

Stain is applied to wood before any sort of sealer

stain enhances the color of wood to bring out grain

different densities of wood absorb the stain at different rates

paint, varnish, lacquer seal out water after a stain is applied.

Lately stain is hard to find the one step idea stain,sealer, clearcoat all in one is the norm the results are so much inferior i have no idea how they can sell that junk.

perhaps that is why you can find so much nice furniture on trash day