  Stability, dark energy (DE) parameterization and swampland aspects for the
Bianchi form-$VI_{h}$ universe have been formulated in an extended gravity
hypothesis. Here we have assumed a minimally coupled geometry field with a
rescaled function of $f(R, T)$ replaced in the geometric action by the Ricci
scalar $R$. Exact solutions are sought under certain basic conditions for the
related field equations. For the following theoretically valid premises, the
field equations in this scalar-tensor theory have been solved. It is observed
under appropriate conditions that our model shows a decelerating to
accelerating phase transition property. Results are observed to be coherent
with recent observations. Here, our models predict that the universe's rate of
expansion will increase with the passage of time. The physical and geometric
aspects of the models are discussed in detail. In this model, we also analyze
the parameterizations of dark energy by fitting the EoS parameter $\omega(z)$
with redshift. The results obtained would be useful in clarifying the
relationship between dark energy parameters. In this, we also explore the
correspondence of swampland dark energy. The swampland criteria have also been
shown the nature of the scalar field and the potential of the scalar field.
