Found some code I had assembled previously:
// get keys for type layer’s style;
// based on code by michael l hale;
// 2014, use it at your own risk;
#target photoshop
if (app.documents.length > 0) {
if (app.activeDocument.activeLayer.kind == LayerKind.TEXT) {
var ref = new ActionReference();
ref.putEnumerated( charIDToTypeID("Lyr "), charIDToTypeID("Ordn"), charIDToTypeID("Trgt") );
var layerDesc = executeActionGet(ref);
var textDesc = layerDesc.getObjectValue(stringIDToTypeID('textKey'));
var paragraphStyle = textDesc.getList(stringIDToTypeID('paragraphStyleRange'));
var kernRange = textDesc.getList(stringIDToTypeID('kerningRange'));
var rangeList = textDesc.getList(stringIDToTypeID('textStyleRange'));
var theFonts = new Array;
for (var m = 0; m < rangeList.count; m++) {
var styleDesc = rangeList.getObjectValue(m).getObjectValue(stringIDToTypeID('textStyle'));
var aFont = styleDesc.getString(stringIDToTypeID('fontPostScriptName'));
// check if font is already in array;
var theCheck = true;
for (var n = 0; n < theFonts.length; n++) {
if (theFonts[n] == aFont) {theCheck = false}
};
if (theCheck == true) {theFonts.push(aFont)}
};
alert (theFonts.join("\n"));
}
};