A problem asks, if you have a positive $\Delta S$ (positive change in entropy) for an exothermic (meaning a negative $\Delta H$, or negative change in enthalpy) reaction and temperature increased, what would happen to $K_{\mathrm{eq}}$ and $K_{\mathrm{eq}}/Q$ (where $K_\mathrm{eq}$ is the equilibrium constant and $Q$ is the reaction quotient)?
The answer states that $K_{\mathrm{eq}}/Q$ and $K_{\mathrm{eq}}$ would increase. This is because if you use the thermodynamic equation, $\Delta G = \Delta H - T \Delta S$ (where $\Delta G$ is the change in Gibbs free energy and $T$ is for temperature), as you increase temperature you get a more negative number (since $\Delta S$ is positive and $T\Delta S$ is being subtracted). This would lead to a more negative $\Delta G$. Then, using another thermodynamic equation, $\Delta G = RT\ln(Q/K_{\mathrm{eq}})$ (where $R$ is the ideal gas constant), if $\Delta G$ is decreasing (becoming more negative), then the term $(Q/K_{\mathrm{eq}})$ must also be going down. This means that $K_{\mathrm{eq}}/Q$ must be going up and therefore $K_{\mathrm{eq}}$ increases, as temperature increases for this exothermic reaction.
So my issue is, I thought for an exothermic reaction, where heat can be represented as a product, I thought increasing the temperature would shift the reaction to the left and decrease $K_{\mathrm{eq}}$. Could someone clarify this for me? I tried looking this up with Chemistry Libretexts, but it didn't seem to clarify anything. The table seemed to suggest that we do use heat as a component of the reaction in endothermic or exothermic reactions to predict the $K_\mathrm{eq}$ change.