Oh, ok, I see. Please pardon my ignorance! I found Affinity Photo from a web search on "free photoshop alternative", and somehow my reading of other posts (as the one mentioned above) didn't reveal to me that Designer was a separate thing.
Okay, so I got the Designer 10-day trail version, and indeed this behaves as expected. And, if I copy & paste a text-along-path from Designer into Photo, then I can still edit the text & path in Photo.
As for buying Designer...it looks great and I'd like to, but I'm working on a print project and will ultimately need to output PDF/X-4 files, which it seems Designer doesn't do (yet). So for now, looks like it's not the 'Illustrator Killer' app I was hoping for...and needing :-(. I'd be happy to buy Designer instead of signing up for Adobe CC if the PDF/X-4 support will happen soon (??). Otherwise...guess I gotta buy Illustrator or impose upon friends that already have it.