I've always known that liner as a J mold or J hook liner since it's an upside down J. That's also what it was sold to me as.
Those clips over the top of it aren't bead receivers, so a beaded liner would also require you to get the bead receivers.
I personally really like the J mold liners, yours has those plastic clip pieces to hold it in place there, mine doesn't because the upright and toprail structure of my pool is completely dufferent, I have blow molded resin pieces, they are solid but hollow, shaped with a groove to overlap the top of the wall and pinch the liner onto the wall - like a "built in clip".
I'd also be spending the time to find the hole....from what I'm seeing, your water is about 2 feet deep right now, it hasn't been dropping for a while (clean side above waterline) so it's relatively safe to say your hole is most likely within 4-6 inches of the water line. I'd dump in some bleach, stir it up with your leaf net, clear up the water, get in and start hunting from the water line down - start where your steps normally go, higher chance of the hole being there than anywhere else.