Auto merge files

This old thread was just bumped and a new topic split off, however, it reminded me that I should update my previous script offering with something a little better (as a beginner in scripting, it looks like I have made some progress in the last 4 months when I compare the two scripts hacked from great sources):

//community.adobe.com/t5/photoshop/auto-merge-files/m-p/10753387
// Auto merge files

// Reference code:
// https://forums.adobe.com/thread/2116421
// https://forums.adobe.com/message/8597315#8597315

#target photoshop

var folder1 = Folder.selectDialog("Please select the base folder with files to process");  // input folder 1
var folder2 = Folder.selectDialog("Please select the layered folder with files to process");  // input folder 2 
var saveFolder = Folder.selectDialog("Please select the folder to save to...");  // output follder
var searchMask = '*.???';
var list1 = folder1.getFiles(searchMask);
var list2 = folder2.getFiles(searchMask);
list1.sort(); // Alpha-numeric sort
list2.sort(); // Alpha-numeric sort

app.displayDialogs = DialogModes.NO;

var psdOptions = new PhotoshopSaveOptions();
psdOptions.embedColorProfile = true;
psdOptions.alphaChannels = true;
psdOptions.layers = true;
psdOptions.spotColors = true;

for (var i = 0; i < list1.length; i++) {
    var doc = open(list1[i]);
    var docName = doc.name;
    placeFile(list2[i], 100);
    doc.activeLayer.blendMode = BlendMode.MULTIPLY; //change blend mode  
    doc.saveAs(new File(saveFolder + '/' + docName.split('.')[0] + '.psd'), psdOptions);
    doc.close(SaveOptions.DONOTSAVECHANGES);
};

alert('Script completed!' + '\n' + 'Files saved to:' + '\r' + saveFolder.fsName);

function placeFile(file, scale) {
    try {
        var idPlc = charIDToTypeID("Plc ");
        var desc2 = new ActionDescriptor();
        var idnull = charIDToTypeID("null");
        desc2.putPath(idnull, new File(file));
        var idFTcs = charIDToTypeID("FTcs");
        var idQCSt = charIDToTypeID("QCSt");
        var idQcsa = charIDToTypeID("Qcsa");
        desc2.putEnumerated(idFTcs, idQCSt, idQcsa);
        var idOfst = charIDToTypeID("Ofst");
        var desc3 = new ActionDescriptor();
        var idHrzn = charIDToTypeID("Hrzn");
        var idPxl = charIDToTypeID("#Pxl");
        desc3.putUnitDouble(idHrzn, idPxl, 0.000000);
        var idVrtc = charIDToTypeID("Vrtc");
        var idPxl = charIDToTypeID("#Pxl");
        desc3.putUnitDouble(idVrtc, idPxl, 0.000000);
        var idOfst = charIDToTypeID("Ofst");
        desc2.putObject(idOfst, idOfst, desc3);
        var idWdth = charIDToTypeID("Wdth");
        var idPrc = charIDToTypeID("#Prc");
        desc2.putUnitDouble(idWdth, idPrc, scale);
        var idHght = charIDToTypeID("Hght");
        var idPrc = charIDToTypeID("#Prc");
        desc2.putUnitDouble(idHght, idPrc, scale);
        var idAntA = charIDToTypeID("AntA");
        desc2.putBoolean(idAntA, true);
        executeAction(idPlc, desc2, DialogModes.NO);

    }
    catch (e) { }
}//end function placeFile

JJMack's scripts are good for this task. I have used Multi Image Collage with 2 white alpha channels that are the size of the entire canvas. I modified one of his scripts for a similar purpose here:

https://community.adobe.com/t5/photoshop/batch-automating-sequences-of-images/m-p/10619866#M263871

The links in that topic have now changed...

https://github.com/MarshySwamp/Layer-Stack-N-Number-of-Files-Filename-as-Top-Layer

Another alternative is to use the script below, it is not 100% of what you are looking for, however, it could be modified...

It expects a single input folder, with filename pairs that alphabetically sort correctly, such as 1-1.png + 1-2.png and 2-1.png + 2-2.png etc.

The second file will be stacked on top set to multiply blend mode.

The script currently saves to a named subfolder in the input folder in JPEG format. This is easily changed.

// Blend File Pairs 1-1.jpg + 1-2.jpg and create 1-3.jpg in Sub Directory
// https://www.photoshopgurus.com/forum/threads/loading-all-images-in-a-folder-into-groups-of-3-is-it-possible.64634/ - Paul MR
// https://forums.adobe.com/thread/2144091
// https://forums.adobe.com/message/11236820#11236820

#target photoshop

var restoreDialogMode = app.displayDialogs;
app.displayDialogs = DialogModes.NO;

main();  
function main(){  
inputFolder = Folder.selectDialog("Please select the folder with Files to process");  
if(inputFolder == null) return;  
var newPath = Folder(decodeURI(inputFolder +"/Merged"));  // Create sub-dir titled "Merged"
if(!newPath.exists) newPath.create();  
var fileList = inputFolder.getFiles(/\.(png)$/i);  // Limit to only .png file input
fileList.sort(); // Force alpha-numeric list sort
while(fileList.length){  
    for(var a =0; a<2;a++){  // Digit 2 for two files
    try{  
    app.open(fileList.pop());  
    }catch(e){}  
        }  
    saveAll();  
    }  
function saveAll(){  
try{  
var Name = app.documents[0].name.replace(/\.[^\.]+$/, '').replace(/-2/, '-3');  // First regex remove file extension, second regex rename from -2 to -3

activeDocument=documents[1];  
activeDocument.activeLayer.duplicate(documents[0]);  
activeDocument = documents[0];  
activeDocument.activeLayer.name=documents[1].name.replace(/\.[^\.]+$/, ''); 

var doc = app.activeDocument;
doc.activeLayer.blendMode = BlendMode.MULTIPLY; // Multiply blend mode

app.displayDialogs = restoreDialogMode;

}catch(e){}  
var saveFile = File(newPath+"/"+Name+".jpg");  
SaveJPG(saveFile);  
  while (app.documents.length) {  
    app.activeDocument.close(SaveOptions.DONOTSAVECHANGES);  
  }  
    }  
}  
function SaveJPG(saveFile){  
var jpgOptions = new JPEGSaveOptions();    
jpgOptions.quality = 8;      
jpgOptions.embedColorProfile = true;
jpgOptions.formatOptions = FormatOptions.STANDARDBASELINE;
jpgOptions.matte = MatteType.NONE;
activeDocument.saveAs(saveFile, jpgOptions, true, Extension.LOWERCASE);  
}  

Data-driven graphics.

https://helpx.adobe.com/photoshop/using/creating-data-driven-graphics.html

Interesting Problem!
Since I´m not familiar with scripting (which should be easy for a scripting-expert?) I tried to find another solution for your problem.
I use Photoshop 19 in german language, so I´m not always quite sure about the correct terminology in english...

1. Create a new Photoshop-File with the size of your images (I presume that they all have the same size).
Perhaps you have to rename your files so Photoshop will read them in correct order (For example 0_00.png -> 0_000.png)
2. Select Files/Videolayers/"New Videolayer from File". Navigate to your first Image-Folder, select the first File (0_000.png) and don´t forget to check "Imagesequence" in the bottom of the dialog.
4. Select Window/Timeline to see what happened: Photoshop created a Videolayer with one Frame for each of your images
5. Now import a Videosequence of the images in your second folder in the same way. In the Timeline you should see the new layer. According images should show up in the same frame. Play around with the navigation-buttons in the top-left of the timeline-window to check for errors
6. If everything is ok, click File/Export/Render video
In the dialog first choose a default file-name and select a folder for the export. Then select "Photoshop Image Sequence" (not "Media-Encoder"), the image-format and quality and some naming options for the files that will be generated. The setting for document-framerate seems to be irrelevant.
Select "All frames" and start the rendering.

I hope that helps and is replicable for you.
Sorry for my bad english 🙂

edit: just saw JJMacks comment: perhaps the scripting-solution would be more flexible...

If the files are exactly the same size,and the images align perfectly, and have the white backgrounds as the PNG files in your post, and the two folders sort the files in the same order. I believe I could create a mockup template that my script would populate your images with and save the merged images as jpeg files with white backrgpinds.  Note that is a lot of AND.

How are you distinguishing which files are merged: different folders, baming conventions,  etc?