  In this paper, we have revisited a class of coupled dark energy models where
dark energy interacts with dark matter via phenomenological interactions. We
included correction terms on the perturbation equations taking into account the
perturbation of the Hubble rate, which was absent in previous works. We also
consider more recent data sets such as cosmic microwave background (CMB)
anisotropies from \textit{Planck} 2018, type I-a supernovae (SNIa) measurements
from Pantheon+ and data from baryon acoustic oscillations (BAO), and redshift
space distortions (RSD). One of the models presents a strong incompatibility
when different cosmological datasets are used. We analyzed the influence of the
SH0ES Cepheid host distances on the results and, although for one model the
discrepancy of $H_0$ is reduced to $1.3\sigma$ when compared to $\Lambda$CDM
and $4.6\sigma$ when compared to the SH0ES team, joint analysis is
incompatible. Including BAO with RSD shows incompatibility with SH0ES for all
models considered here. We performed a model comparison, but there is no clear
preference for interacting dark energy over $\Lambda$CDM ($|\Delta \chi^2|<1$
for all the models for joint analysis CMB+BAO+RSD+SNIa). We conclude that the
models of interactions in the dark sector considered in this paper are not
flexible enough to fit all the cosmological data including values of $H_0$ from
SH0ES in a statistically acceptable way, either the models would need to be
modified to include further flexibility of predictions or that there remains a
tension in this coupled dark energy paradigm.
