Your assumption is correct. However, following your first response last night, which it seems you have expanded upon since, I granted permission to access the Playlist folder in my old phone and repeated the Export function from the Playlist folder and it worked. I then copied the Playlists to my computer and, in turn, copied them back to my new phone.
I understand in that process the root portion of each Playlist file's path changed but in the end, the final Folder and file names remained intact. (with the exception in the file names where I had a "/" in some of the names, which was replaced in the final path with " _".
In your Rexnord conversation you said, "If you move the M3U8 file to another device, or perhaps a computer, you may need to adjust the first ("root") part of the path details. For example, another Android device will have a different name for its SD Card. Instead of D0D8-84ED, and a PC might need a very different root path path such as "C:\Users\youraccountname\ Music\...". Some apps may try to work it out the differences for themselves (Poweramp can do that). So if you have a PC-based M3U or M3U8 file which you copy over to your phone's music folder, as long as the final folder name and the filename match correctly, Poweramp should be able to resolve and find the same audio file on your phone."
Unfortunately, even though I have rescanned both the Library, in general, and the Playlist folder, specifically, it still "Doesn't look like anything to me."
Your insight has moved me much closer, but I am still short of the finish line. Can you help me over?
Or, should I try repeating the process using the Export/Import functions from the general Settings menu? If so, once I connect the 2 phones together, designating the Playlist folder in the old phone to be imported into the new phone has presented a new challenge.
Thank you very much!!