Electrical detection of topological magnetic textures such as skyrmions is currently limited to conducting materials. While magnetic insulators offer key advantages for skyrmion technologies with high speed and low loss, they have not yet been explored electrically. Here, we report a prominent topological Hall effect in Pt/Tm$_3$Fe$_5$O$_{12}$ bilayers, where the pristine Tm$_3$Fe$_5$O$_{12}$ epitaxial films down to 1.25 unit cell thickness allow for tuning of topological Hall stability over a broad range from 200 to 465 K through atomic-scale thickness control. Although Tm$_3$Fe$_5$O$_{12}$ is insulating, we demonstrate the detection of topological magnetic textures through a novel phenomenon: spin-Hall topological Hall effect (SH-THE), where the interfacial spin-orbit torques allow spin-Hall-effect generated spins in Pt to experience the unique topology of the underlying skyrmions in Tm$_3$Fe$_5$O$_{12}$. This novel electrical detection phenomenon paves a new path for utilizing a large family of magnetic insulators in future skyrmion technologies.