We search for signatures of cosmological shocks in gas pressure profiles of galaxy clusters using the cluster catalogues from three surveys: the Dark Energy Survey (DES) Year 3, the South Pole Telescope (SPT) SZ survey, and the Atacama Cosmology Telescope (ACT) data releases 4, 5, and 6, and using thermal Sunyaev-Zeldovich (SZ) maps from SPT and ACT. The combined cluster sample contains around 105 clusters with mass and redshift ranges $10^{13.7} \lt M_{\rm 200m}/\, {\rm M}_\odot \lt 10^{15.5}$ and 0.1 < z < 2, and the total sky coverage of the maps is $\approx 15\, 000 \deg ^2$. We find a clear pressure deficit at R/R200m ≈ 1.1 in SZ profiles around both ACT and SPT clusters, estimated at 6σ significance, which is qualitatively consistent with a shock-induced thermal non-equilibrium between electrons and ions. The feature is not as clearly determined in profiles around DES clusters. We verify that measurements using SPT or ACT maps are consistent across all scales, including in the deficit feature. The SZ profiles of optically selected and SZ-selected clusters are also consistent for higher mass clusters. Those of less massive, optically selected clusters are suppressed on small scales by factors of 2-5 compared to predictions, and we discuss possible interpretations of this behaviour. An oriented stacking of clusters - where the orientation is inferred from the SZ image, the brightest cluster galaxy, or the surrounding large-scale structure measured using galaxy catalogues - shows the normalization of the one-halo and two-halo terms vary with orientation. Finally, the location of the pressure deficit feature is statistically consistent with existing estimates of the splashback radius.