Lookback time resolves Hubble tension? A recent axiv paper by Capozziello et al (27 Feb 2023) claims:

the H0 tension is not due to neither systematic errors, nor to some new physics beyond the $\Lambda$CDM model, but simply to the fact that, in measuring the same quantity at different redshift, different results arise thanks to the look-back time evaluated at different epochs.

Now, maybe the solution is really this "simple", and I might be missing something, but I thought the age of the universe/lookback times depend on input cosmological parameters, including the Hubble parameter, i.e. just the redshift isn’t enough. Noting this paper claims the age of the universe by Planck collaboration was derived without using $H_0$ via six independent parameters.
How can Capozziello et al claim stack up?
It would seem to me to be a reheated version of this claim by the same author.
 A: Their equation (5) says
$$T_{lt} = T_0 − T(z) = T_0 − a(t)T_0$$
where $T_{lt}$ is the light travel time and $T_0$ is the present age of the universe. That implies they're assuming $T=a\,T_0$. In a footnote they say

The parametrization $T(z) = a(t)T_0$ is assumed as a label for the age of the Universe at a given redshift.

Fine, but you can't do that and also equate $T$ with the cosmological time, which they do.
They could be equated in a Milne cosmology, where $a\propto t$. It may be true that Milne cosmology is a better fit to this data, but Milne cosmology requires either $Ω\approx 0$, which is strongly excluded by other data, or general relativity being wrong. The paper claims to resolve the tension within the standard ΛCDM model, so it's just wrong.
A: Look back time also known as light-travel distance isn't well defined, so it doesn't make sense to use it for astronomical calculations.
For more information please see Edward Wright's Article https://astro.ucla.edu/~wright/Dltt_is_Dumb.html
I can't see these points discussed in the reference you show.
