Large-scale inter-combustor thermoacoustic interactions occur frequently in modern can-annular gas turbine combustion systems due to the presence of an annular cross-talk section upstream of the first stage turbine stator vanes. Although the whole system's modal dynamics depend on the relative dominance of low-frequency planar or high-frequency transverse acoustic waves, the majority of prior studies have chiefly focused on longitudinal mode instabilities. Motivated by the paucity of detailed information, here we examine high-frequency transverse acoustic interactions between two adjacent lean-premixed hydrogen combustors connected via two different pathways, known as cross-fire (XF) and cross-talk (XT) sections. We observe that the dual-combustor system undergoes high-frequency spinning mode in the clockwise direction, manifested as well-defined limit cycles with peak-to-peak amplitude of around 10 kPa. The transverse pressure oscillations, in contrast to the well-established low-frequency mutual synchronization dynamics, are not fully synchronized even in the presence of cross-talk communication. This situation leads to the formation of two closely-spaced 1T modes at 4.76 and 4.86 kHz in the respective hydrogen combustors, accompanied by the beating of the pressure fluctuations solely in the XF tube section. Remarkably, the pressure waves induced near the XF tube section tend to lag behind the pressure waves spinning in the injector face, demonstrating the existence of the angular shift characteristically connected to the high-frequency transverse combustion dynamics.