We report on a series of highly resolved large-eddy simulations of the LS89 high-pressure turbine (HPT) vane, varying the exit Mach number between Ma = 0.7 and 1.1. In order to accurately resolve the blade boundary layers and enforce pitchwise periodicity, we for the first time use an overset mesh method, which consists of an O-type grid around the blade overlapping with a background H-type grid. The simulations were conducted either with a synthetic inlet turbulence condition or including upstream bars. A quantitative comparison shows that the computationally more efficient synthetic method is able to reproduce the turbulence characterictics of the upstream bars. We further perform a detailed analysis of the flow fields, showing that the varying exit Mach number significantly changes the turbine efficiency by affecting the suction-side transition, blade boundary layer profiles, and wake mixing. In particular, the Ma = 1.1 case includes a strong shock that interacts with the trailing edge, causing an increased complexity of the flow field. We use our recently developed entropy loss analysis (Zhao and Sandberg, GT2019-90126) to decompose the overall loss into different source terms and identify the regions that dominate the loss generation. Comparing the different Ma cases, we conclude that the main mechanism for the extra loss generation in the Ma = 1.1 case is the shock-related strong pressure gradient interacting with the turbulent boundary layer and the wake, resulting in significant turbulence production and extensive viscous dissipation.