stix2, overline and superscripts

Consider the following MWE without stix2 loaded (looks nice with and without overline):

And with stix2 loaded (looks nice without but horrible with overline):

The overline is placed a bit high, but my main issue is that the superscript is placed far too high for some reason. A very similar problem was reported and fixed in this question, but it uses XeLaTeX (I’m using pdflatex) and the proposed solution using wideoverbar does not appear to be available for use with pdflatex?

Is this a bug? Can I fix it somehow?

MWE code:

documentclass{article}

%usepackage{stix2}
usepackage{amsmath}

newcommand*{tran}{^{mkern-1.5mumathsf{T}}}

begin{document}
    
begin{equation*}
    h tran s qquad h^2 s
end{equation*}

begin{equation*}
    overline{h}tran overline{s} qquad overline{h}^2 overline{s}
end{equation*}
    
end{document}