Custom shape list in latest version of Photoshop.

Is that what you want？

alert(getPresetList());
 
function getPresetList(){  
var ref = new ActionReference();   
   ref.putEnumerated( charIDToTypeID("capp"), charIDToTypeID("Ordn"), charIDToTypeID("Trgt") );   
   var appDesc = executeActionGet(ref);   
  var List = appDesc.getList(stringIDToTypeID('presetManager'));  
   
  var presetNames=[];  
    var list = List.getObjectValue(6).getList(charIDToTypeID('Nm  '));  
    // alert( list.getType(0));  
    for (var i = 0; i < list.count; i++) {  
      var str = list.getString(i);  
      str += "\n";
   //   logInfo(str)
      presetNames.push(str);  
    }  
return presetNames;  
}  

Sure in X's Xtool in its App folder there is a s script "PresetLister.js"  the will list all preset including Custom shapes.   Custom shapes can have duplicate names as other custom shaped the also have a unique identifier.  However, in Photoshop 2020 Adobe made some changes that seems to have broken things like scripts. There now a Shapes Palette that has groups of shapes. Script that I have theat add Shape by Name using Action manager code still work.

var SB = activeDocument.activeLayer.bounds;
//var SB = app.activeDocument.selection.bounds;		// Get the bounds of the selection
top=SB[1].value;
left=SB[0].value;
bottom=SB[3].value;
right=SB[2].value;
rc=top + ":" + left + ":" + bottom + ":" + right;
Name="Chris";
Name= prompt("Shape Name ",Name);
addShape(Name,rc); 

function addShape(name,bounds) {
	top=bounds.substr(0,bounds.indexOf(":")); bounds=bounds.substr(bounds.indexOf(":")+1);
	left=bounds.substr(0,bounds.indexOf(":")); bounds=bounds.substr(bounds.indexOf(":")+1);
	bottom=bounds.substr(0,bounds.indexOf(":")); right=bounds.substr(bounds.indexOf(":")+1);
	// Add a Shape at resolution Black Fill no stroke
var idMk = charIDToTypeID( "Mk  " );
    var desc139 = new ActionDescriptor();
    var idnull = charIDToTypeID( "null" );
        var ref69 = new ActionReference();
        var idcontentLayer = stringIDToTypeID( "contentLayer" );
        ref69.putClass( idcontentLayer );
    desc139.putReference( idnull, ref69 );
    var idUsng = charIDToTypeID( "Usng" );
        var desc140 = new ActionDescriptor();
        var idType = charIDToTypeID( "Type" );
            var desc141 = new ActionDescriptor();
            var idClr = charIDToTypeID( "Clr " );
                var desc142 = new ActionDescriptor();
                var idRd = charIDToTypeID( "Rd  " );
                desc142.putDouble( idRd, 0.000000 );
                var idGrn = charIDToTypeID( "Grn " );
                desc142.putDouble( idGrn, 0.000000 );
                var idBl = charIDToTypeID( "Bl  " );
                desc142.putDouble( idBl, 0.000000 );
            var idRGBC = charIDToTypeID( "RGBC" );
            desc141.putObject( idClr, idRGBC, desc142 );
        var idsolidColorLayer = stringIDToTypeID( "solidColorLayer" );
        desc140.putObject( idType, idsolidColorLayer, desc141 );
        var idShp = charIDToTypeID( "Shp " );
            var desc143 = new ActionDescriptor();
            var idNm = charIDToTypeID( "Nm  " );
            desc143.putString( idNm, name );
            var idTop = charIDToTypeID( "Top " );
            var idPxl = charIDToTypeID( "#Pxl" );
            desc143.putUnitDouble( idTop, idPxl, top );
            var idLeft = charIDToTypeID( "Left" );
            var idPxl = charIDToTypeID( "#Pxl" );
            desc143.putUnitDouble( idLeft, idPxl, left );
            var idBtom = charIDToTypeID( "Btom" );
            var idPxl = charIDToTypeID( "#Pxl" );
            desc143.putUnitDouble( idBtom, idPxl, bottom );
            var idRght = charIDToTypeID( "Rght" );
            var idPxl = charIDToTypeID( "#Pxl" );
            desc143.putUnitDouble( idRght, idPxl, right );
        var idcustomShape = stringIDToTypeID( "customShape" );
        desc140.putObject( idShp, idcustomShape, desc143 );
        var idstrokeStyle = stringIDToTypeID( "strokeStyle" );
            var desc144 = new ActionDescriptor();
            var idstrokeStyleVersion = stringIDToTypeID( "strokeStyleVersion" );
            desc144.putInteger( idstrokeStyleVersion, 2 );
            var idstrokeEnabled = stringIDToTypeID( "strokeEnabled" );
            desc144.putBoolean( idstrokeEnabled, false );
            var idfillEnabled = stringIDToTypeID( "fillEnabled" );
            desc144.putBoolean( idfillEnabled, true );
            var idstrokeStyleLineWidth = stringIDToTypeID( "strokeStyleLineWidth" );
            var idPnt = charIDToTypeID( "#Pnt" );
            desc144.putUnitDouble( idstrokeStyleLineWidth, idPnt, 2.000000 );
            var idstrokeStyleLineDashOffset = stringIDToTypeID( "strokeStyleLineDashOffset" );
            var idPnt = charIDToTypeID( "#Pnt" );
            desc144.putUnitDouble( idstrokeStyleLineDashOffset, idPnt, 0.000000 );
            var idstrokeStyleMiterLimit = stringIDToTypeID( "strokeStyleMiterLimit" );
            desc144.putDouble( idstrokeStyleMiterLimit, 100.000000 );
            var idstrokeStyleLineCapType = stringIDToTypeID( "strokeStyleLineCapType" );
            var idstrokeStyleLineCapType = stringIDToTypeID( "strokeStyleLineCapType" );
            var idstrokeStyleButtCap = stringIDToTypeID( "strokeStyleButtCap" );
            desc144.putEnumerated( idstrokeStyleLineCapType, idstrokeStyleLineCapType, idstrokeStyleButtCap );
            var idstrokeStyleLineJoinType = stringIDToTypeID( "strokeStyleLineJoinType" );
            var idstrokeStyleLineJoinType = stringIDToTypeID( "strokeStyleLineJoinType" );
            var idstrokeStyleMiterJoin = stringIDToTypeID( "strokeStyleMiterJoin" );
            desc144.putEnumerated( idstrokeStyleLineJoinType, idstrokeStyleLineJoinType, idstrokeStyleMiterJoin );
            var idstrokeStyleLineAlignment = stringIDToTypeID( "strokeStyleLineAlignment" );
            var idstrokeStyleLineAlignment = stringIDToTypeID( "strokeStyleLineAlignment" );
            var idstrokeStyleAlignInside = stringIDToTypeID( "strokeStyleAlignInside" );
            desc144.putEnumerated( idstrokeStyleLineAlignment, idstrokeStyleLineAlignment, idstrokeStyleAlignInside );
            var idstrokeStyleScaleLock = stringIDToTypeID( "strokeStyleScaleLock" );
            desc144.putBoolean( idstrokeStyleScaleLock, false );
            var idstrokeStyleStrokeAdjust = stringIDToTypeID( "strokeStyleStrokeAdjust" );
            desc144.putBoolean( idstrokeStyleStrokeAdjust, false );
            var idstrokeStyleLineDashSet = stringIDToTypeID( "strokeStyleLineDashSet" );
                var list13 = new ActionList();
            desc144.putList( idstrokeStyleLineDashSet, list13 );
            var idstrokeStyleBlendMode = stringIDToTypeID( "strokeStyleBlendMode" );
            var idBlnM = charIDToTypeID( "BlnM" );
            var idNrml = charIDToTypeID( "Nrml" );
            desc144.putEnumerated( idstrokeStyleBlendMode, idBlnM, idNrml );
            var idstrokeStyleOpacity = stringIDToTypeID( "strokeStyleOpacity" );
            var idPrc = charIDToTypeID( "#Prc" );
            desc144.putUnitDouble( idstrokeStyleOpacity, idPrc, 100.000000 );
            var idstrokeStyleContent = stringIDToTypeID( "strokeStyleContent" );
                var desc145 = new ActionDescriptor();
                var idClr = charIDToTypeID( "Clr " );
                    var desc146 = new ActionDescriptor();
                    var idRd = charIDToTypeID( "Rd  " );
                    desc146.putDouble( idRd, 85.998688 );
                    var idGrn = charIDToTypeID( "Grn " );
                    desc146.putDouble( idGrn, 37.003326 );
                    var idBl = charIDToTypeID( "Bl  " );
                    desc146.putDouble( idBl, 17.999725 );
                var idRGBC = charIDToTypeID( "RGBC" );
                desc145.putObject( idClr, idRGBC, desc146 );
            var idsolidColorLayer = stringIDToTypeID( "solidColorLayer" );
            desc144.putObject( idstrokeStyleContent, idsolidColorLayer, desc145 );
            var idstrokeStyleResolution = stringIDToTypeID( "strokeStyleResolution" );
            desc144.putDouble( idstrokeStyleResolution, 182.880005 );
        var idstrokeStyle = stringIDToTypeID( "strokeStyle" );
        desc140.putObject( idstrokeStyle, idstrokeStyle, desc144 );
    var idcontentLayer = stringIDToTypeID( "contentLayer" );
    desc139.putObject( idUsng, idcontentLayer, desc140 );
executeAction( idMk, desc139, DialogModes.NO );

}

CC 2019 still works