Investigating cosmic distance duality and dark energy evolution through intermediate and high-{\it z} probes

We investigate deviations from the cosmic distance duality relation adopting model-dependent and -independent approaches using i) a Taylor expansion, ii) a power-law parameterization, iii) a logarithmic correction, iv) a [Formula: see text] Padé polynomial and v) a second order Chebyshev parameterization. We derive constraints on all parameters using observational Hubble data, galaxy clusters, type Ia supernovae, DESI data and gamma-ray bursts. Through Monte-Carlo Markov chain analyses adopting the Metropolis Hastings algorithm, we find no significant violation of duality, then model selection criteria favor flat scenarios even though a slight curvature is not totally ruled out. For the [Formula: see text] tension we find a preference at [Formula: see text]-[Formula: see text] for [Formula: see text] from supernovae when dropping DESI data and for [Formula: see text] from Planck when using DESI and gamma-ray bursts.