The other option is see if you can just fit a a 3.5mm jack in there. Then its never an issue again and if they get pulled on it just disconnects. Also usb 2.0 cables have enof wires for this (4) fyi and there cheap and easy to get hold of.

Idellly pull the staple and replace string but, realistically buy some liquid electrical tape and paint over the cut. https://www.amazon.com/Gardner-Bender-07315001126-LTB-400-Electrical/dp/B000FPAN2K/

yeah yt can find some interesting music some times... I was listing to ether halestore or greenday well, it dug up this artist the other day all of her music just confuses me more. https://youtu.be/Zokn4WDPcHE?t=101

I would probably just cut the walls and run the outlet. Drywall repair is not a big deal. You can probably even do it with only one small patch. Search how to do it but basically you use a scrap bit of wood on the back side to to bridge the gap then screw the patch into it.

I would cut a small hole above the existing outlet probably 4-6 inches go sideways though probably 2-3 studs based on your drawing then stick an outlet in the closet with a old work box, for your 12v lighting.

https://www.homedepot.com/p/Carlon-14-cu-in-PVC-Old-Work-Electrical-Outlet-Box-1-Gang-B114RB/100404027

You just need a long flexible drill bit to go sideways.

https://www.homedepot.com/p/Klein-Tools-3-Piece-Flexible-Drill-Bit-Kit-53721/203913339

Another option is what's on the other side of the closet if its another room there might be an outlet on the other side if so this gets way easer. As you can bascily cut a hole in the same wall cavity (between studs)as existing outlet and the hole will be where the new outlet is. You just make Shure you use you don't cut in the exact same spot as the existing outlet.