I couldn't find any information how the stroke-width is transformed...
Up to know I thought the final stroke-width is calculated using the scalings of all groups and the path - see the svg code below:
1) scaling of 'g0001' * scaling of 'path0011'  * stroke-width  * dpi = 1 * 1 * 0.0002604in * 96 = 0.025 mm -> confirmed by incscape
2) scaling of 'g0002' * scaling of 'g0012' * scaling of 'path0112'  * stroke-width  * dpi = 0 * 1 * 0.00344 * 0.22213928in * 96 = 0 ??? But incscape shows 0.025 mm
   If I leave out the '0' from the matrix in 'g0002': 1 * 0.00344 * 0.22213928in * 96 = 0.073359

Does anyone knows, how the stroke-width transform works?

The code:

<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<!-- Created with Inkscape (http://www.inkscape.org/) -->

<svg
   width="22.535355mm"
   height="24.070175mm"
   viewBox="0 0 22.535355 24.070175"
   version="1.1"
   id="svg821"
   sodipodi:docname="test.svg"
   inkscape:version="1.1.1 (3bf5ae0d25, 2021-09-20)"
   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
   xmlns="http://www.w3.org/2000/svg"
   xmlns:svg="http://www.w3.org/2000/svg"
   xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
   xmlns:cc="http://creativecommons.org/ns#"
   xmlns:dc="http://purl.org/dc/elements/1.1/">
  <g
     transform="translate(2.4999999,-272.96518)"
     id="layer1"
     inkscape:groupmode="layer"
     inkscape:label="1">
    <g
       transform="translate(3.7163734,0.02505583)"
       id="g0001">
      <path
         inkscape:connector-curvature="0"
         d="m -4.9547318,288.6345 -0.036035,-0.0726 -0.1104309,-0.11122 h 0.7695287"
         style="fill:none;stroke:#000000;stroke-width:0.0002604in;stroke-linecap:round;stroke-linejoin:round"
         id="path0011" />
    </g>
    <g
       id="g0002"
       transform="matrix(0,-0.34364983,0.33801784,0,-95.940701,281.19026)"
       style="fill:none;stroke:#000000;stroke-width:2.93408108;stroke-linecap:round;stroke-linejoin:round"
       inkscape:label="Hershey Text">
      <g
         id="g0012"
         transform="translate(-6.9999995,279)"
         style="stroke-width:2.93408108">
        <path
           id="path0112"
           transform="scale(0.00344,-0.00344)"
           style="stroke-width:0.22213928in"
           d="m 220,504 v 32 l 32,62 32,32 62,32 h 126 l 64,-32 31,-32 31,-62 V 472 L 567,410 504,315 189,0 h 441"
           inkscape:connector-curvature="0" />
      </g>
    </g>
  </g>
</svg>