How to save a photo from Photos to desktop and keep the photo's original taken date?

Put another way:

There are two kinds of metadata involved when you consider jpeg or other image file.

One is the file data. This is what the Finder shows. This tells you nothing about the contents of the file, just the File itself.

The problem with File metadata is that it can easily change as the file is moved from place to place or exported, e-mailed, uploaded etc.

Photographs have also got both Exif and IPTC metadata. The date and time that your camera snapped the Photograph is recorded in the Exif metadata. Regardless of what the file date says, this is the actual time recorded by the camera.

Photo applications like Photos, CaptureOne, Lightroom, Mylio, Photoshop etc get their date and time from the Exif metadata.

When you export from iPhoto to the Finder a new file is created containing your Photo (and its Exif). The File date is - quite accurately - reported as the date of Export.

However, the Photo Date doesn't change.

The problem is that the Finder doesn't work with Exif.

So, your photo has the correct date, and so does the file, but they are different things. To sort on the Photo date you'll need to use a photo app.

There are apps that will edit the file data to match the Exif. This is one:

https://www.publicspace.net/ABetterFinderAttributes/index.html

The Finder is a tool to handle files, not photos. The file creation date in the Finder is showing the date the file has been created on your computer, not necessarily the date the picture has been taken. But the capture date, when the photo has been taken will be embedded in the EXIF tags of the image file. It is not lost. when you open the photo with an image editor you will see the capture date.

• When you export a file with "File > Export > Export unmodified original", the file creation date may be the date the file has been imported to Photos for Mac, but if you are using iCloud Photos, the file creation date may change to the date the file has been downloaded from iCloud.
• When you export a file with "File > Export > Export .. photos" Photos will render the current version with all adjustments applied as a new file, and this new exported file will always have the date of export as the file creation date.

You can see the the date the photo has been taken in the Finder, if you are using macOS 10.14 or later. Then the Finder will also be showing the tag "Content created", when you view the finder window in column view.

For example, a folder in column view: (my Mac ist to use the German language, but you can see, that in addition to the creation date, modification date, last opened date of today the content creation date is also shown, showing an earlier date).

You can also see the "content created" date in Preview, if you open the Inspector.

There are tools to copy the capture date to the file creation date, for examplyGraphic converter or Raw Right Away.