This explanation for why dG < 0 (under constant p & T) implies spontaneity is simple enough. But when the internal energy also depends on other things besides entropy and volume (i.e. non-mechanical work) it seems like the condition dG = Q - TdS + (other work-terms) < 0 will no longer be equivalent with TdS > dQ. This seems to matter when we are dealing with chemical reactions since the expressions for dU will contain a term for chemical potentials.

I'm probably just misunderstanding something simple