  We provide novel constraints on the parameters defining the universal
pressure profile (UPP) within clusters of galaxies, and explore their
dependence on the cluster mass and redshift, from measurements of
Sunyaev-Zel'dovich Compton-$y$ profiles. We employ both the $\textit{Planck}$
2015 MILCA and the ACT-DR4 $y$ maps over the common $\sim 2,100\,\text{deg}^2$
footprint. We combine existing cluster catalogs based on KiDS, SDSS and DESI
observations, for a total of 23,820 clusters spanning the mass range
$10^{14.0}\,\text{M}_{\odot}<M_{500}<10^{15.1}\,\text{M}_{\odot}$ and the
redshift range $0.02<z<0.98$. We split the clusters into three independent bins
in mass and redshift; for each combination we detect the stacked SZ cluster
signal and extract the mean $y$ angular profile. The latter is predicted
theoretically adopting a halo model framework, and MCMCs are employed to
estimate the UPP parameters, the hydrostatic mass bias $b_{\rm h}$ and possible
cluster miscentering effects. We constrain $[P_0,c_{500},\alpha,\beta]$ to
$[5.9,2.0,1.8,4.9]$ with $\textit{Planck}$ and to $[3.8,1.3,1.0,4.4]$ with ACT
using the full cluster sample, in agreement with previous findings. We do not
find any compelling evidence for a residual mass or redshift dependence, thus
expanding the validity of the cluster pressure profile over much larger
$M_{500}$ and $z$ ranges; this is the first time the model has been tested on
such a large (complete and representative) cluster sample. Finally, we obtain
loose constraints on the hydrostatic mass bias in the range 0.2-0.3, again in
broad agreement with previous works.
