How to Preserve Created or Modified Date on non-photograph PNG images in batch processing?

I  have found lots of discussions on this forum about preserving EXIF data for camera RAW and JPEG file type, and this doesn't seem to apply to my PNG filetype. I have seen statements that this is "normal" behavior. In that case, I guess I'm doing something outside the norm (but not too far because there are others asking about how to do this as well)

By @CodeSlayer2010

Technically (somebody correct this if wrong), it might not be EXIF metadata you need to preserve, but one of the common file system date types; I am guessing you only need to preserve the file creation date. This would not be EXIF-specific metadata because EXIF is typically generated by cameras. This might be why some say it’s “normal”…EXIF is not expected to be in a PNG if it was not created by a camera. A screen shot would be expected to include the same file Date Created and Date Modified found in all computer files. If it had EXIF, it would also include Date Taken (Capture Date). That’s a camera image creation date and time that’s recorded separately so that it can be preserved even as a photo is edited and exported or converted (which creates a new Date Created and Date Modified, as you are seeing). Date Taken can be maintained throughout that process; but again, a PNG normally doesn’t have Date Taken.

Stephen_A_Marsh’s ExifTool solution might be the way to go, because ExifTool is cross platform, free, very well known and trusted (used by many applications), and appears to do the job. If I read his example correctly, the command line is not actually doing anything with EXIF (appropriate since there is probably not any EXIF-specific info in the PNGs), but just transferring a PNG original’s file system Date Created and Date Modified to the converted JPG copies. This sort of specialized need is an example of a reason people often turn to ExifTool. If using the command line is challenging, I understand that there are some graphical front ends to ExifTool out there.

The command line interface ExifTool program can easily do this for a batch of images in say two different folders:

https://exiftool.org/forum/index.php?topic=10322.0

Here is an example on the Mac:

exiftool -TagsFromFile /Users/username/Desktop/My_Folder/PNG/%f.png -FileCreateDate -FileModifyDate /Users/username/Desktop/My_Folder/JPG

Without detailed knowledge it seems to me that if you are converting PNG to JPG, the solution is to do nothing with a PNG when the JPG already exists.