Photoshop Batch Editing with Automate Issue

Normally the way a Batch action work is they are used by  Batch Processor either Photoshop File>Autmate>Batch..., or Photoshop menu File>Script>BatchScriptName... like Image processor,  or menu File>Automate>BatchPlug-inName... like Image processor pro....  The Batch processor work on a file list of the image files to be Batch.  And uses your Batch Action in the processing of the files being processed by the batch processor.  Your Batch Action would not load the current image into your Phot image Psd template that has a logo layer in a corner  that would replace the Photo templates image for there no way your action can save the changed layer document it open with the name of the image the action pasted into the layered document. Actions can not use the logic required to do processing like that.  If your Image file are the size you want all you action  needs to do is place your logo into its corner sized  for the current document's size.

I have posted a script that you cans easly edit to use  your logo file and you  cans use that script in your batch action to place in logoe sized and position for you images.   PlaceLogp.jsx

/* ==========================================================
// 2021  John J. McAssey (JJMack) 
// ======================================================= */
// This script is supplied as is. It is provided as freeware. 
// The author accepts no liability for any problems arising from its use.
/*
<javascriptresource>
<about>$$$/JavaScripts/PlaceLogo/About=JJMack's PlaceLogo ^r^rCopyright 2021 Mouseprints.net^r^rPhotoshop Script^rCustomize using first four var</about>
<category>JJMack's Script</category>
<enableinfo>true</enableinfo>
</javascriptresource>
*/
#target photoshop;  
app.bringToFront();  
var logoFile = "~/Desktop/JJMack.png";				// Logo Image file should be large for resize down works better than up. Vector files can be any size.
var LogoSize = 10;											// percent of document height to resize Logo to
var LogoMargin = 1;                                         // percent of Document height the Logo should have as a margin
var LogoLocation = 9;										// Like a tick tack toe board 1 through 9.  1=Top Left 9=Bottom Right
var LogoRotation = -20;										// Center Logo Location 5 can be Rotated -90 through +90 degrees  + degree Clockwise - CounterClockwise

app.displayDialogs = DialogModes.NO;				// Dialog off 
var strtRulerUnits = app.preferences.rulerUnits;	// Save Users ruler units 
var strtTypeUnits = app.preferences.typeUnits;		// Save Users Type units 
app.preferences.rulerUnits = Units.PIXELS;			// work with pixels 
app.preferences.typeUnits = TypeUnits.PIXELS;		// work with pixels 
//placeLogo(logoFile, LogoSize, LogoMargin, LogoLocation, LogoRotation); // Place Logo into the location 5 would be Document's center
if (documents.length) app.activeDocument.suspendHistory('placeLogo','placeLogo(logoFile,LogoSize,LogoMargin, LogoLocation, LogoRotation)' );
app.preferences.rulerUnits = strtRulerUnits;		// Restore user ruler units  
app.preferences.typeUnits = strtTypeUnits;			// Restore user type units    
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
function placeLogo(Image,Size,Margin,position,angle){  
	if(!documents.length) return;  							// if no document return
	var fileObj = new File(Image);	 		               	// the passed file
	if(!fileObj.exists){  									// If file does not exits tell user 
		alert(fileObj.name  + " does not exist!"); 			// Alert User 
		return;  											// return
	}  
	try{  
		var doc = app.activeDocument;						// set Doc object to active document
		var layers = app.activeDocument.layers;				// get layers
		app.activeDocument.activeLayer = layers[0];			// Target Top Layer
		placeFile(fileObj); 								// Place in file the Logo File
		activeDocument.activeLayer.resize(100 ,100,AnchorPosition.MIDDLECENTER); // Insure Place did not scale layer  
		var SB = activeDocument.activeLayer.bounds; 		// get layers bounds 
		var layerHeight = SB[3] - SB[1];					// get layers height  
		var resizePercent = (100/layerHeight)*(Size/100*doc.height.value); // Percent to resize by 
		activeDocument.activeLayer.resize(resizePercent ,resizePercent,AnchorPosition.MIDDLECENTER);  // Resize width and height by percentage 
		marginSize = Margin/100*doc.height.value;			// Margin size
		var selectedRegion = Array(Array(0+marginSize,0+marginSize), Array(doc.width-marginSize,0+marginSize), Array(doc.width-marginSize,doc.height-marginSize), Array(0+marginSize,doc.height-marginSize));
		activeDocument.selection.select(selectedRegion);    // Select  document area for the logo Positioning
		switch (position){									// Align resized logo smart object layer into position
			case 1 : align('AdLf'); align('AdTp'); break;
			case 2 : align('AdCH'); align('AdTp'); break;
			case 3 : align('AdRg'); align('AdTp'); break;
			case 4 : align('AdLf'); align('AdCV'); break;
			case 5 : align('AdCH'); align('AdCV'); activeDocument.selection.deselect(); activeDocument.activeLayer.rotate(angle); break;
			case 6 : align('AdRg'); align('AdCV'); break;
			case 7 : align('AdLf'); align('AdBt'); break;
			case 8 : align('AdCH'); align('AdBt'); break;
			case 9 : align('AdRg'); align('AdBt'); break;
			default : break;
		}
		app.activeDocument.selection.deselect();			// deselect
	}
	catch(e) { alert(e + ': on line ' + e.line); }			// inform user of error  
	finally{ }  
} 
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////// 
function placeFile(placeFile) {  
    var desc21 = new ActionDescriptor();  
    desc21.putPath( charIDToTypeID('null'), new File(placeFile) );  
    desc21.putEnumerated( charIDToTypeID('FTcs'), charIDToTypeID('QCSt'), charIDToTypeID('Qcsa') );  
    var desc22 = new ActionDescriptor();  
    desc22.putUnitDouble( charIDToTypeID('Hrzn'), charIDToTypeID('#Pxl'), 0.000000 );  
    desc22.putUnitDouble( charIDToTypeID('Vrtc'), charIDToTypeID('#Pxl'), 0.000000 );  
    desc21.putObject( charIDToTypeID('Ofst'), charIDToTypeID('Ofst'), desc22 );  
    executeAction( charIDToTypeID('Plc '), desc21, DialogModes.NO );  
} 

function align(method) {
	var desc = new ActionDescriptor();
	var ref = new ActionReference();
	ref.putEnumerated( charIDToTypeID( "Lyr " ), charIDToTypeID( "Ordn" ), charIDToTypeID( "Trgt" ) );
	desc.putReference( charIDToTypeID( "null" ), ref );
	desc.putEnumerated( charIDToTypeID( "Usng" ), charIDToTypeID( "ADSt" ), charIDToTypeID( method ) );
	try{
		executeAction( charIDToTypeID( "Algn" ), desc, DialogModes.NO );
	}catch(e){}
}