  Disequilibrium chemistry due to vertical mixing in the atmospheres of many
brown dwarfs and giant exoplanets is well-established. Atmosphere models for
these objects typically parameterize mixing with the highly uncertain $K_{\rm
zz}$ diffusion parameter. The role of mixing in altering the abundances of
C-N-O-bearing molecules has mostly been explored for solar composition
atmospheres. However, atmospheric metallicity and the C/O ratio also impact
atmospheric chemistry. Therefore, we present the \texttt{Sonora Elf Owl} grid
of self-consistent cloud-free 1D radiative-convective equilibrium model
atmospheres for JWST observations, which includes a variation of $K_{\rm zz}$
across several orders of magnitude and also encompasses sub-solar to
super-solar metallicities and C/O ratios. We find that the impact of $K_{\rm
zz}$ on the $T(P)$ profile and spectra is a strong function of both $T_{\rm
eff}$ and metallicity. For metal-poor objects $K_{\rm zz}$ has large impacts on
the atmosphere at significantly higher $T_{\rm eff}$ compared to metal-rich
atmospheres where the impact of $K_{\rm zz}$ is seen to occur at lower $T_{\rm
eff}$. We identify significant spectral degeneracies between varying $K_{\rm
zz}$ and metallicity in multiple wavelength windows, in particular at 3-5
$\mu$m. We use the \texttt{Sonora Elf Owl} atmospheric grid to fit the observed
spectra of a sample of 9 early to late T- type objects from $T_{\rm
eff}=550-1150$ K. We find evidence for very inefficient vertical mixing in
these objects with inferred $K_{\rm zz}$ values lying in the range between
$\sim$ 10$^1$-10$^4$ cm$^2$s$^{-1}$. Using self-consistent models, we find that
this slow vertical mixing is due to the observations probing mixing in the deep
detached radiative zone in these atmospheres.
