Hans suggested to textext() each desired snippet individually. So I tried

---
\setupbodyfont[10pt]



\starttext


\startMPinclusions
    pickup pencircle scaled 0.05pt;
    defaultpen := savepen;
    
    picture crosshair;
    crosshair := image(draw fullcircle scaled 2pt;
                       draw (0,-2pt)--(0,2pt);
                       draw (-2pt,0)--(2pt,0);
                      );
    
    bboxmargin := 0;
\stopMPinclusions



\startMPpage    
    for item within rawtextext("$(h,g)$"):
        draw bbox item withcolor 0.8white;
        draw item;
    endfor;
    
    draw crosshair;
\stopMPpage


\startMPpage    
    draw bbox rawtextext("$($") withcolor 0.8white;
    draw rawtextext("$($");
    
    draw bbox rawtextext("$h$") withcolor 0.8white;
    draw rawtextext("$h$");
    
    draw bbox rawtextext("$,$") withcolor 0.8white;
    draw rawtextext("$,$");
    
    draw bbox rawtextext("$g$") withcolor 0.8white;
    draw rawtextext("$g$");
    
    draw bbox rawtextext("$)$") withcolor 0.8white;
    draw rawtextext("$)$");
    
    draw crosshair;
\stopMPpage


\stoptext
---

Clearly, this gives me each glyph individually but stacked on top of each other. What I need though is that the second figure looks exactly like the first one (with all glyphs in the right location) except that the grey bounding boxes appear per glyph.

Thanks for your help,
Oliver