[Help] Drywall 1.5" x 20" L-shaped hole repair?

I was wondering if using 2" mesh joint tape + mud would be a good solution for fixing this hole in our bathroom, or if I should replace using patch repair board. The gap is 1.5" tall, and 20" long. Thanks in advance. [Edit:] Update, I cut out a larger rectangle out of the wall and cut drywall to match. I screwed one half of the new drywall into existing joist on the right, but the joist that's all chewed up on the left is too far back to screw into. I tried screwing wood into the side of the screwed up joist to screw the drywall into, but that's still too far back. So half the new drywall is secure, but the corner is not.I'm thinking I will cut an even taller piece of the wall out so I have access to the left-hand joist that's not all jacked up.[Edit 2:] That worked well. Am I right that I can use this mesh construction joint tape on the seams, mud over it, and sand to finish?Also those two round holes in the mirror wall, would using the mesh joint tape + mud work for that, too? Thanks in advance.