Dimensions of nodes

Question

In the following picture, I would like to use the same width for the rounded rectangles and the same height for the arrows (take a look at the last ones).

To do that I need to store the dimensions of the nodes used. Is there an easy way to do that?

documentclass{article}

usepackage{nicematrix,tikz}
usetikzlibrary{shapes.misc, calc}

% Source: https://tex.stackexchange.com/a/585865/6880
newcommandtest[2]{%
    #1 & {} = {} & #2 [8mm]
}

newcommandstep[3]{
    draw [->,shorten < = 1pt, shorten > = 1pt]
           let p1 = ([xshift=-1mm]#2-1.south east) ,
               p2 = ([yshift=1mm]#3-1.north) 
           in (p1) -- (x1,y2) ;
    draw [->,shorten < = 1pt, shorten > = 1pt]
           let p1 = ([xshift=1mm]#2-3.south west) ,
               p2 = ([yshift=1mm]#3-3.north) 
           in (p1) -- (x1,y2) ;
    node [draw, fill=white, rounded rectangle] at ([yshift=-5mm]#2-2){tinykern1em$#1$kern1em} ;
}

begin{document}

$begin{NiceArray}{r@{}c@{}l}
    test{2x+3}{5x-4}
    test{2x  }{5x-7}
    test{-3x }{-7}
    test{x   }{dfrac73}
    CodeAfter
    begin{tikzpicture}
        step{-3}{1}{2}
        step{-5x}{2}{3}
        step{div (-3)}{3}{4}
    end{tikzpicture}
 end{NiceArray}$

 end{document}

dimensions nodes tikz pgf

Daniel N · Accepted Answer

Update
I thought about a different solution that solves the problem of the arrows' length and at the same time, allows a normal code for the equations.

The code
documentclass[12pt, a4paper]{article}
usepackage{amsmath}
usepackage{tikz}

newcommand{action}[1]{%
  &= tikz[baseline=-.5ex]{%
    path[use as bounding box] (0, -3ex) rectangle ++(1pt, 6ex);
    draw[->] (-3.5ex, 3ex) -- ++(0, -6ex);
    draw[->] (.5ex, 3ex) -- ++(0, -6ex);
    path (-1.5ex, 0)
    node[draw, rectangle, rounded corners, fill=WG, thin,
    inner sep=1ex, minimum width=11ex, scale=.7] {$#1$};
  }
}
definecolor{WG}{RGB}{217, 221, 221}

begin{document}
begin{align*}
  2x +3 &= 5x -4 
  action{3} 
  2x &= 5x -7 
  action{-5x} 
  -3x &= -7 
  action{div(-3)} 
  x &= frac{7}{3}
end{align*}
end{document}

First solution
I'm proposing a solution based on nodes (in TikZ).  It is true that the alignment of = is lost.  It might be retrieved by breaking the equations into pieces further, but I don't know if you are interested.  Eventually, you can transform it into a LaTeX command.

The height of each wide node is fixed such that the fraction fits into it.
The arrows have the same length since they connect nodes at equal distances.
There is a parameter d which controls the horizontal space between the arrows.

The code
documentclass[11pt, margin=1cm]{standalone}
usepackage{tikz}
usetikzlibrary{calc, math} 
usetikzlibrary{fit, positioning, arrows.meta}
usetikzlibrary{backgrounds}

begin{document}
definecolor{WG}{RGB}{217, 221, 221}
tikzset{
  w/.style={minimum width=22ex, minimum height=6ex},
  n/.style={draw, rectangle, rounded corners,
    fill=white, thick,
    inner sep=1ex, minimum width=10ex, scale=.7},
  m/.style={->, shorten <=-3pt, shorten >=-2.75pt}
}
tikzmath{
  real d, il, ol, ie, oe;
  d = 35;
  ol = 270 -d;  il = 90 +d;
  oe = 270 +d;  ie = 90 -d;
}
begin{tikzpicture}[node distance=1ex and 5ex,
  every node/.style={text=black}]
  node[w] (Iw) {$2x +3 = 5x -4$};
  node[below=of Iw, n] (In) {$-3$};
  node[below=of In, w] (IIw) {$2x = 5x -7$};
  node[below=of IIw, n] (IIn) {$-5x$};
  node[below=of IIn, w] (IIIw) {$-3x = -7$};
  node[below=of IIIw, n] (IIIn) {$div(-3)$};
  node[below=of IIIn, w] (IVw) {$x = frac{7}{3}$};

begin{pgfonlayer}{background}
    node[gray, fill=WG, fit=(Iw) (IVw), inner sep=0pt] {};
    draw
    (Iw.ol) edge[m] (IIw.il)
    (Iw.oe) edge[m] (IIw.ie)
    (IIw.ol) edge[m] (IIIw.il)
    (IIw.oe) edge[m] (IIIw.ie)
    (IIIw.ol) edge[m] (IVw.il)
    (IIIw.oe) edge[m] (IVw.ie);
  end{pgfonlayer}
end{tikzpicture}

end{document}

Dimensions of nodes

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