  The James Webb Space Telescope (JWST) is reporting unexpectedly massive high
redshift galaxies that appear challenging from the $\Lambda$CDM perspective.
Interpreted as a problem of cosmological origin, this necessitates Planck
underestimating either matter density $\Omega_m$ or physical matter density
$\Omega_m h^2$ at higher redshifts. Through standard frequentist profile
likelihoods, we identify corroborating quasar (QSO) and gamma-ray burst (GRB)
data sets where $\Omega_m$ increases with effective redshift
$z_{\textrm{eff}}$, with $\Omega_m$ remaining anomalously large at higher
redshifts. While the variation of $\Omega_m$ with $z_{\textrm{eff}}$ is at odds
with the $\Lambda$CDM model, demarcating frequentist confidence intervals
through differences in $\chi^2$ in profile likelihoods, the prevailing
technique in the literature, points to $3.9 \sigma$ and $7.9 \sigma$ tensions
between GRBs and QSOs, respectively, and Planck-$\Lambda$CDM. We explain the
approximations inherent in the existing profile likelihood literature, and
highlight fresh methodology that generalises the prescription. We show that
alternative methods, including Bayesian approaches, lead to similar tensions.
