Maths symbols and unicode-math input inside siunitx commands

You can add other comparators to the default list:

\documentclass{article}

\usepackage{siunitx}
\usepackage{unicode-math}

\sisetup{
  input-comparators = {
    < = > \approx \ge \geq \gg \le \leq \ll \sim % default
    \gtrsim ≳ ≈
  },
}

\begin{document}

\SIrange{≳9}{≈40}{\kilogram}

\SIrange{\gtrsim9}{\approx40}{\kilogram}

\end{document}

You could set parse-numbers to false to allow arbitrary code in the number fields:

\documentclass{standalone}

\usepackage{siunitx}
\usepackage{unicode-math}

\begin{document}
  \SIrange[parse-numbers = false]{≳9}{≈40}{\kilogram}\\
  \SIrange[parse-numbers = false]{\gtrsim9}{\approx40}{\kilogram}
\end{document}

Or, you could declare the symbols explicitly in \sisetup:

\documentclass{standalone}

\usepackage{siunitx}
\sisetup{
  input-symbols=≈≳\gtrsim\approx
}
\usepackage{unicode-math}

\begin{document}
  \SIrange{≳9}{≈40}{\kilogram}\\
  \SIrange{\gtrsim9}{\approx40}{\kilogram}
\end{document}