The full-sky measurements of the cosmic microwave background (CMB) temperature anisotropies by WMAP and Planck have highlighted several unexpected isotropy-breaking features on the largest angular scales. We investigate the impact of the local large-scale structure on these anomalies through the thermal and kinetic Sunyaev-Zeldovich effects. We used a constrained hydrodynamical simulation that reproduced the local Universe in a box of 500 h−1 Mpc to construct full-sky maps of the temperature anisotropies produced by these two secondary effects of the CMB, and we discuss their statistical properties on large angular scales. We show the significant role played by the Virgo cluster on these scales, and we compare it to theoretical predictions and random patches of the Universe obtained from the hydrodynamical simulation Magneticum. We explored three of the main CMB large-scale anomalies, that is, the lack of a correlation, the quadrupole-octopole alignment, and the hemispherical asymmetry, in the latest Planck data (PR4), where they are detected at a level similar to the previous releases. We also use the simulated secondaries from the local Universe to verify that their impact is negligible.