Attacking the problem from a completely different angle... if your font does not support auto-scaling of brackets etc., are you open to the scalerel package which has a \scaleleftright[]{}{}{} command for mimicking the scale-to-size feature I think you are seeking? In the case of scalerel, it takes the base character and scales it directly to match the height of the target object. But here's the trick: the optional argument is a width limiter, to prevent the scaled object from getting too wide. In this example, I set that argument to 2ex, so that no matter how big the character is scaled, it never gets wider than 2ex.

Alternatively, there is \stretchleftright command which does a vertical stretch, but in that case, it has an aspect-ratio limiter as the optional argument, so that the aspect ratio of the stretched symbol never exceeds the amount given in the optional argument.

In all cases, the auto-scaled object is based on the original font symbol.

\documentclass{article}
\usepackage{scalerel}
\parskip 2ex
\begin{document}
\(
\scaleleftright[2ex]{[}{ x^2}{]}
\scaleleftright[2ex]{(}{ x^2}{)}
\scaleleftright[2ex]{\{}{ x^2}{\}}
\)

\(
\scaleleftright[2ex]{[}{%
\begin{array}{c}%
 x^2\\
y^2\\
\end{array}}{]}
\scaleleftright[2ex]{(}{%
\begin{array}{c}%
 x^2\\
y^2\\
\end{array}}{)}
\scaleleftright[2ex]{\{}{%
\begin{array}{c}%
 x^2\\
y^2\\
\end{array}}{\}}
\)

\(
\scaleleftright[2ex]{[}{%
\begin{array}{c}%
 x^2\\
y^2\\
z^2\\
\end{array}}{]}
\scaleleftright[2ex]{(}{%
\begin{array}{c}%
 x^2\\
y^2\\
z^2\\
\end{array}}{)}
\scaleleftright[2ex]{\{}{%
\begin{array}{c}%
 x^2\\
y^2\\
z^2\\
\end{array}}{\}}
\)

\end{document}

Just for comparison, below I use the \stretchleftright command, rather than the \scaleleftright

Go to view->themes->fontsize

it works