  Recent cosmological tensions, in particular, to infer the local value of the
Hubble constant $H_0$, have developed new independent techniques to constrain
cosmological parameters in several cosmologies. Moreover, even when the
concordance Cosmological Constant Cold Dark Matter ($\Lambda$CDM) model has
been well constrained with local observables, its physics has shown deviations
from a flat background. Therefore, to explore a possible deviation from a flat
$\Lambda$CDM model that could explain the $H_0$ value in tension with other
techniques, in this paper we study new cosmological constraints in spatial
curvature dark energy models. Additionally, to standard current Supernovae Type
Ia (SNIa) catalogs, we extend the empirical distance ladder method through an
SNIa sample using the capabilities of the James Webb Space Telescope (JWST) to
forecast SNIa up to $z \sim 6$, with information on the star formation rates at
high redshift. Furthermore, we found that our constraints provide an
improvement in the statistics associated with $\Omega_{m}$ when combining SNIa
Pantheon and SNIa Pantheon+ catalogs with JW forecasting data.
