How to get the name and the path of the font used in photoshop (not textItem.font)

You could try this as it looks as if you are using Windows.

Run the VBS script to create a fontlist file on the desktop.

Then run the javaScript on the PSD document.

It should copy the fonts to the same folder as the document, it will also create a text file with a list of fonts.

It didn't find all the fonts in my test psd maybe because it wasn't in the windows/font folder?

VBS.

Set wshShell = WScript.CreateObject("WScript.Shell")
Set wshSysEnv = wshShell.Environment("PROCESS")
sMyFile = "c:" & wshSysEnv("HOMEPATH") & "\Desktop\Fontlist.txt"
Dim objFileSystem, objOutputFile
Dim strOutputFile
Set objFileSystem = CreateObject("Scripting.fileSystemObject")
Set objOutputFile = objFileSystem.CreateTextFile(sMyFile, TRUE)

Dim str
Const HKEY_LOCAL_MACHINE = &H80000002
strComputer = "."

Set objReg=GetObject("winmgmts:{impersonationLevel=impersonate}!\\" & _
strComputer & "\root\default:StdRegProv")

strKeyPath = "Software\Microsoft\Windows NT\CurrentVersion\Fonts"
objReg.EnumValues HKEY_LOCAL_MACHINE, _
strKeyPath,arrEntryNames,arrEntryZZZ

For Each entry in arrEntryNames
str = wshshell.RegRead("HKLM\Software\Microsoft\Windows NT\CurrentVersion\Fonts\" & entry)

       objOutputFile.WriteLine(entry & "," & str)
Next
objOutputFile.Close

javaScript.

#target photoshop;
app.bringToFront();

main();
function main(){
if(!documents.length) return;
try{
var Path = activeDocument.path;
}catch(e){
    alert("This document needs to be saved before running this script!");
    return;
    }
var FontFile = File(Folder.desktop + "/FontList.txt");
if(!FontFile.exists){
    alert("You need to run the vbs script first to create the FontList file!");
    return;
    }
var FontList = new Array();
    FontFile.open('r') ; 
while(!FontFile.eof){   
   strInputLine =FontFile.readln(); 
   if (strInputLine.length > 3) inputArray  = strInputLine.split(","); 
   if(inputArray.length == 2) FontList.push([[inputArray[0]],[inputArray[1]]]);
   }
FontFile.close();
var PSDtextLayers = getNamesPlusIDs();
PSDtextLayers = UniqueSortedList(PSDtextLayers);
for(var a in PSDtextLayers){
    for(var f in FontList){
         var rex = new RegExp;
         rex = PSDtextLayers.toString();

        if(FontList[1].toString().match(rex,"i")){
            var From = new File("/c/windows/fonts/" + FontList[1].toString());
            var To = new File(Path + "/"+  FontList[1].toString());
            From.copy(To);
            break;
            }
        }
    }
var rFonts = new File(Path + "/required Fonts.txt");
rFonts.open('w');
rFonts.write(PSDtextLayers.join('\n'));
rFonts.close();
};
function UniqueSortedList(ArrayName){
var unduped = new Object;
for (var i = 0; i < ArrayName.length; i++) {   
unduped[ArrayName] = ArrayName;

}
var uniques = new Array;for (var k in unduped) {
   uniques.push(unduped);}
return uniques;
}
function getNamesPlusIDs(){ 
   var ref = new ActionReference(); 
   ref.putProperty( charIDToTypeID( "Prpr" ), charIDToTypeID( 'NmbL' ));
   ref.putEnumerated( charIDToTypeID('Dcmn'), charIDToTypeID('Ordn'), charIDToTypeID('Trgt') ); 
   var count = executeActionGet(ref).getInteger(charIDToTypeID('NmbL')) +1; 
   var Names=[];
try{
    activeDocument.backgroundLayer;
var i = 0; }catch(e){ var i = 1; };
   for(i;i<count;i++){ 
       if(i == 0) continue;
        ref = new ActionReference(); 
        ref.putIndex( charIDToTypeID( 'Lyr ' ), i );
        var desc = executeActionGet(ref);
        var layerName = desc.getString(charIDToTypeID( 'Nm  ' ));
        var Id = desc.getInteger(stringIDToTypeID( 'layerID' ));
        if(layerName.match(/^<\/Layer group/) ) continue;
        if (desc.hasKey(stringIDToTypeID('textKey'))){
            desc = desc.getObjectValue(stringIDToTypeID('textKey'));
            desc = desc.getList(stringIDToTypeID('textStyleRange')).getObjectValue(0).getObjectValue(stringIDToTypeID('textStyle'));
            var postScriptName = desc.getString( stringIDToTypeID('fontPostScriptName'));      
Names.push(postScriptName);
}
   }; 
return Names;
};

I would even say what you propose is not allowed/intended behavior of platform fonts. Fonts are very much licensed/DRM-constrained content, i.e. either Apple/Microsoft or the user has a contract on the use of the file (you pay separately for web/app/print use) and redistribution is not permitted even in free fonts. So assuming you want to copy the so it could be distributed with the PSD without careful examination of the terms, you're likely to be on shaky legal ground. I would study if you could for example convert textItems to shapes, etc. to be portable.