This Letter presents the result of a $3+1$ sterile neutrino search using 10.7 yr of IceCube data. We analyze atmospheric muon neutrinos that traverse the Earth with energies ranging from 0.5 to 100 TeV, incorporating significant improvements in modeling neutrino flux and detector response compared to earlier studies. Notably, for the first time, we categorize data into starting and throughgoing events, distinguishing neutrino interactions with vertices inside or outside the instrumented volume, to improve energy resolution. The best-fit point for a $3+1$ model is found to be at ${\sin }^2\left(2{\theta }_{24}\right)=0.16$ and $\Delta m_{41}^2=3.5{\mathrm{eV}}^2$, which agrees with previous iterations of this Letter. The result is consistent with the null hypothesis of no sterile neutrinos with a $p$ value of 3.1%.