  In this study, we investigate deviations from the Planck-$\Lambda$CDM model
in the late universe ($z \lesssim 2.5$) using the Gaussian Processes method,
with minimal assumptions. Our goal is to understand where exploring new physics
in the late universe is most relevant. We analyze recent Cosmic Chronometers
(CC), Type Ia Supernovae (SN), and Baryon Acoustic Oscillations (BAO) data. By
examining reconstructions of the dimensionless parameter $\delta(z)$, which
measures deviations of the Hubble parameter from the Planck-$\Lambda$CDM
predictions, we identify intriguing features at low ($z \lesssim 0.5$) and high
($z \gtrsim 2$) redshifts. Deviations from the Planck-$\Lambda$CDM model were
not significant between $0.5\lesssim z \lesssim2$. Using the combined CC+SN+BAO
dataset, we gain insights into dark energy (DE) dynamics, resembling
characteristics of omnipotent DE, extending beyond quintessence and phantom
models. DE exhibits n-quintessence traits for $z\gtrsim2$, transitioning with a
singularity around $z\sim2$ to usual phantom traits in $1\lesssim z\lesssim2$.
DE characteristics differ between scenarios ($H_0$-SH0ES and
$H_0$-$\Lambda$\&CMB), with $H_0$-SH0ES leaning towards phantom traits and
$H_0$-$\Lambda$\&CMB towards quintessence. We suggest exploring new physics at
$z\lesssim0.5$ and $1.5\lesssim z\lesssim2.5$, particularly around $z = 2$, to
understand cosmological tensions such as $H_0$ and $S_8$.
