I believe the connector you have is this https://www.amazon.com/Tiger-Inspired-LED-Connector-Terminal/dp/B07QJ4HVZ8
It's got screw terminals for your power wires and then clamps down on the copper contacts of your LED strip.
You'll have to get to the screws which are hidden under that stone tile to remove and replace it. Either your LED strip went bad, the connector went bad, or something's wrong with the power. Not sure if there's a transformer on the other end of if it's wired directly to a switch.
I would start maybe with a new LED strip since that's the easiest to replace in this situation, then try to get access to the screw terminals and replace the connector. It looks like its probably wired directly to those switches below so I'd look at the wiring inside that switch box.