What is the chemical reason talc is used in water-based paint and not in solvent based paint?
Most water based paints are emulsions of plastics particles dispersed in water, it is common to use vinyl acetate to make polyvinyl acetate. To do this an emulsion of vinyl acetate in water is formed, then by adding a free radical initiator.

One purpose which fine clay can furfill in the paint polymer synthesis is to increase the stability of the emulsion of droplets of the liquid monomer. These clay particles will be incorperated into the final paint.

It is also common to add other inorganic substances such as barium sulfate and titanium dioxide. These are used to make the paint more opaque.

One classic organic based paint class is the alkyd paint, these are made by reacting acid anhydrides such as phthalic and maleic anhydride with a polyalcohol such as glycerol or 2,2-dimethylpropane-1,3-diol under acidic conditions. It is normal to distill water out of the reaction, often an unsaturated fatty acid is added in the form of a glycerol triester (vegtable oil).

The idea is that with glycerol the fatty acid ester will react in a transestification reaction to add pedent groups onto the main polymer. Then when the paint is exposed to oxygen a radical cross linking reaction occurs. The other main option I see is to add some maleic acid to the synthesis of the paint binder. The to add some styrene to the paint. This again will cross link with a radical reaction.

For the alkyd paint synthesis there is no need to add talc, these polymerisations are done under homogenous conditions by heating a close to solvent free mixture of monomers. Rather than being a radical polymerisation (example of an addition polymerisation) this reaction is a condensation polymersation where many small chains are converted into a few long chains.