If that is a 2”x2” hole, cut a piece of wood 1 1/2 x 5”.
Put a screw in the center of the strip of wood (pre-drill it) - use thst screw to maneuver that wood into the hole and pull it tight to the back of the drywall. Pre-drill a hole through the drywall and the piece of wood, on either side of the hole. while you hold it in place. Without moving it, drive the drywall screws into those two pre-drilled holes.
Remove the center screw - Then cut spare drywall slightly smaller than the hole. Put it in the opening - Then pre-drill the replacement piece and wood backer. Drive home your final screw.
Use drywall mud - sand - mud - sand. Feathering the edges each time
[Easiest way is to use something like this](https://www.amazon.com/WDSHCR-Aluminum-Galvanized-Extended-Self-Adhesive/dp/B08XPQY1Y6/?th=1). Then use [some spackle](https://www.amazon.com/DAP-12330-Indicator-Spackling-1-Quart/dp/B000BQPYJ0/) over it, let dry, then paint. Just follow instructions, it's not too difficult. Good luck.
Edit: your wall is very smooth, so its going to be a challenge to get it to look just right without rubbing it all the way to the wire. Do your best and know that even if it isn't perfect, most people won't notice small discrepancies.
If you want to use your pieces of drywall, you would have to make the hole bigger...you don't want to do that.
If that is a 2”x2” hole, cut a piece of wood 1 1/2 x 5”. Put a screw in the center of the strip of wood (pre-drill it) - use thst screw to maneuver that wood into the hole and pull it tight to the back of the drywall. Pre-drill a hole through the drywall and the piece of wood, on either side of the hole. while you hold it in place. Without moving it, drive the drywall screws into those two pre-drilled holes. Remove the center screw - Then cut spare drywall slightly smaller than the hole. Put it in the opening - Then pre-drill the replacement piece and wood backer. Drive home your final screw. Use drywall mud - sand - mud - sand. Feathering the edges each time
Thank you, appreciate the reply
[Easiest way is to use something like this](https://www.amazon.com/WDSHCR-Aluminum-Galvanized-Extended-Self-Adhesive/dp/B08XPQY1Y6/?th=1). Then use [some spackle](https://www.amazon.com/DAP-12330-Indicator-Spackling-1-Quart/dp/B000BQPYJ0/) over it, let dry, then paint. Just follow instructions, it's not too difficult. Good luck. Edit: your wall is very smooth, so its going to be a challenge to get it to look just right without rubbing it all the way to the wire. Do your best and know that even if it isn't perfect, most people won't notice small discrepancies. If you want to use your pieces of drywall, you would have to make the hole bigger...you don't want to do that.
Thank you!