Transferring software from old pc to new [MacBook Pro]

As Abambo says, Elements 15 will not work with any recent Mac OS.  And unless you purchased a boxed disc, it is likely that you bought an OS-specific version of the program which cannot be transferred from Windows to Mac.  You can check the Products page of your Adobe account to see which OS platform you purchased, and a download link will be present there.

You will, however, be eligible for a prior-owner discount if you purchase Elements 2023.

Knowing Apple, the old software will not work on the new computer, even if you will be able to find the macOS download image of the Elements software. I would suppose, that you will need to buy or upgrade the bundle.

See also this thread for moving your software to a new machine: https://community.adobe.com/t5/photoshop-elements-discussions/how-to-deactivate-photoshop-elements/m-p/12407860#M73415

(I will move this to the Photoshop Elements forum, I suppose the problem is similar, regardless of the software, Photoshop or Premier Elements)