Can I use delimiter for brackets of a non-math font in math mode?

Question

MWE:

\documentclass{article}
\usepackage{amsthm, amsmath}
\usepackage{unicode-math}
\setmathfont[,Scale=1,FakeStretch=1,FakeBold=0]{NewCMMath-Book.otf}
\setmathfont[range={"0028, "0029},Scale=1,FakeStretch=1,FakeBold=0]{CenturymodernTT-Regular.otf}
\begin{document}
Some random text
    \begin{align*}
        \log x\left(\pi(x)-\pi\left(\frac{x}{2}\right)\right)
    \end{align*}

1234567890


\end{document}

I have looked at questions that sound similar but aren't really e.g.

applying math formatting to a non-math font

Unicode math at TeX primitive level

Notice how delimiter does not work with parentheses. I think it's because the font does not have math script and does not have the corresponding scaled brackets defined in the font file itself. Is there a way to make use of the delimiter of the usual CM font for this parentheses?

I have tried some scaling mechanism but I did not like the output very much because of alignment issues. To clarify, I would like to use the parentheses like this:

I was able to produce this by editing specific glyphs inside the font. First, I took the NewCM math font, replaced some glyphs with old looking ones. Then I replaced some brackets by some old glyphs and added transformations such as scaling, moving vertically, etc. Unfortunately, even though I edited brackets from v1 to v7 in the glyph table, it did not cover all possible cases which makes the output look like this:

See how some brackets work but some don't (probably the ones that require the most scaling).

Hopefully that gives a good idea of what I want to achieve and what I have tried.

Answer 1

It's unclear what you want.

To begin with, you cannot borrow the parentheses from a non-math font and hope they scale with \left and \right: in order to do this, the font must support the feature and have a MATH table.

Second problem: you say

Is there a way to make use of the delimiter of the usual CM font for this parentheses?

Let's see a few examples.

With NewCMMath only

\documentclass{article}
\usepackage{amsthm, amsmath}
\usepackage{unicode-math}
\setmathfont{NewCMMath-Book.otf}
\begin{document}
Some random text
\begin{equation}
\log x\left(\pi(x)-\pi\left(\frac{x}{2}\right)\right)
\end{equation}
1234567890
\end{document}

With Latin Modern Math for the parentheses

\documentclass{article}
\usepackage{amsthm, amsmath}
\usepackage{unicode-math}
\setmathfont{NewCMMath-Book.otf}
\setmathfont{Latin Modern Math}[range={"0028, "0029}]
\begin{document}
Some random text
\begin{equation}
\log x\left(\pi(x)-\pi\left(\frac{x}{2}\right)\right)
\end{equation}
1234567890
\end{document}

With legacy Computer Modern for the parentheses

\documentclass{article}
\usepackage{amsthm, amsmath}
\usepackage{unicode-math}
\setmathfont{NewCMMath-Book.otf}
\DeclareSymbolFont{CMoperators}{OT1}{cmr} {m}{n}
\SetSymbolFont{operators}{bold}{OT1}{cmr} {bx}{n}
\DeclareSymbolFont{CMlargesymbols}{OMX}{cmex}{m}{n}
\DeclareMathDelimiter{(}{\mathopen} {CMoperators}{"28}{CMlargesymbols}{"00}
\DeclareMathDelimiter{)}{\mathclose}{CMoperators}{"29}{CMlargesymbols}{"01}
\begin{document}
Some random text
\begin{equation}
\log x\left(\pi(x)-\pi\left(\frac{x}{2}\right)\right)
\end{equation}
1234567890
\end{document}

Conclusion

I see no difference at all in the three pictures.