How can ${\mathbf{\Delta S}}^{\mathbf{o}}$be relatively independent of$\mathbf{T}$ if${\mathbf{S}}^{\mathbf{o}}$of each reactant and product increases with $\mathbf{T}$?

Entropy is a measure of a system's unpredictability or disorder in general.

Entropy is a thermodynamic property that describes how a system behaves in terms of temperature, pressure, entropy, and heat capacity.

Entropy is a term used to describe the extent of a disorder. Atoms and particles gain a lot of energy as the physical condition changes, allowing them to move more freely (from solid to liquid or liquid to gas).

Take water from melted ice as an example, which has been heated to boiling temperature to create water vapour.

${\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right)\to {\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right)$

Both liquid and vaporised water become more entropic as the temperature rises. The entropy changes little with temperature between a liquid's melting point and boiling point (water). Since the thermal energy is not sufficient to break the intermolecular interactions ($\mathrm{H}-$bond), the molecules on the water surface are bonded to each other and the entropy change is minimal. So, in such a case, it can be said that the entropy is relatively independent until water is finally reaching its boiling temperature.

Therefore, the entropy $\left({\mathrm{\Delta S}}^{\mathrm{o}}\right)$is relatively independent of $\text{T}$.