  The recent analysis on the central compact object in the HESS J1731-347
remnant suggests interestingly small values for its mass and radius. Such an
observation favors soft nuclear models that may be challenged by the
observation of massive compact stars. In contrast, the recent PREX-II
experiment, concerning the neutron skin thickness of $^{208}$Pb, points towards
stiff equations of state that favor larger compact star radii. In the present
study, we aim to explore the compatibility between stiff hadronic equations of
state (favored by PREX-II) and the HESS J1731-347 remnant in the context of
hybrid stars. For the construction of hybrid equations of state we use three
widely employed Skyrme models combined with the well-known vector MIT bag
model. Furthermore we consider two different scenarios concerning the energy
density of the bag. In the first case, that of a constant bag parameter, we
find that the resulting hybrid equations of state are strongly disfavored by
the observation of $\sim2 M_\odot$ pulsars. However, the introduction of a
Gaussian density dependence yields results that are compatible with the
conservative $2 M_\odot$ constraint. The utilization of recent data based on
the observation of PSR J0030+0451, PSR J0952-0607 and GW190814 allows for the
imposition of additional constraints on the relevant parameters and the
stiffness of the two phases. Interestingly, we find that the derived hybrid
equations of state do not satisfy the PSR J0030+0451 constraints in $1\sigma$
and only marginally agree with the $2\sigma$ estimations. In addition, we
estimate that the observation of massive pulsars, like PSR~J0952-0607, in
combination with the existence of HESS J1731-347, may require a strong phase
transition below $\sim 1.7n_0$. Finally, we show that the supermassive compact
object involved in GW190814 could potentially be explained as a rapidly
rotating hybrid star.
