How to get a `not divides' symbol of the correct size using lualatex and unicode-math package?

Question

I am having problems with \not command. I have read this: unicode-math breaks \not command I have tried the fix mentioned there. This MWE compiles without problems in pdflatex:

\documentclass{article}
\usepackage{amssymb}
\newcommand{\Mod}[1]{\ \left(\mathrm{mod}\ #1\right)}
\begin{document}
    
    \(p^{k+1}\nmid\left(\alpha^2-a\right)\)
     $p^{k+1}\not\left\vert\left(\alpha^2-a\right)\right.$
\end{document}

The first one with \nmid gives a small divides' symbol So, I use \not\left\vert ...\right.to get a largerdivides' symbol. I get the desired output in pdflatex as seen in the screen shot above. So, there is no syntax problem. But, this mwe gives problems in lualatex:

\documentclass{article}
\usepackage{mathtools}
\usepackage{unicode-math}

\ExplSyntaxOn
\def\__um_oldnot:#1{\mathrel{%
        \mathchoice
        {\rlap{$\displaystyle\mkern1mu/$}}%
        {\rlap{$\textstyle\mkern1mu/$}}%
        {\rlap{$\scriptstyle/$}}%
        {\rlap{$\scriptscriptstyle/$}}%
        {#1}}}
\ExplSyntaxOff
\setmathfont{XITS Math Regular}
\newcommand{\Mod}[1]{\ \left(\mathrm{mod}\ #1\right)}
\begin{document}
     \(p^{k+1}\nmid\left(\alpha^2-a\right)\)
     $p^{k+1}\not\left\vert\left(\alpha^2-a\right)\right.$
\end{document}

I get the following error message:

! Missing { inserted.
<to be read again> 
\left 
l.18     $p^{k+1}\not\left
                      \vert\left(\alpha^2-a\right)\right.$
A left brace was mandatory here, so I've put one in.
You might want to delete and/or insert some corrections
so that I will find a matching right brace soon.
If you're confused by all this, try typing `I}' now.

! Missing } inserted.
<inserted text> 
}
l.18 ...not\left\vert\left(\alpha^2-a\right)\right.$
                                                  
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

How to fix this problem.

Edit: @egreg has pointed out that the pdflatex version works by accident of implementation. What is the best way to get a `not divides' symbol of the correct size that works with unicode-maths also?