Cosmological parameters represent fundamental quantities that offer insights into the structure, composition, and dynamics of the universe. Despite the remarkable progress of modern cosmology, significant challenges persist, with cosmological tensions emerging as a focal point. In this talk, I will discuss the results obtained using geometric probes from DESI and galaxy–CMB lensing cross-correlations to test extensions of the standard cosmological model. I will focus on scenarios with either dynamical or interacting dark energy, showing that current observations reveal signatures pointing toward possible new physics in the dark sector beyond the standard cosmological model, while also potentially helping to address existing cosmological tensions.