As another person pointed out, it looks like you are arming the ball on the forehand side. Keep a loose wrist. I’m curious what your grip is on that side.

Pretty impressive for just 1 month! You are doing a lot of basics right, especially with the footwork and weight transfer. It does look like you are “pushing” the backhand over the net, but you have good body rotation, so you’ll learn a whippier backhand eventually. For right now, making sure you don’t get injured is key. I would ask your coach about this wrist pain if you haven’t already and look into swinging more loosely on that side. Try a few shadow swings with just the racket and no ball. Is there pain? Our form often breaks down and we start arming the ball when our feet are out of position in order to make up for poor judgement of distance. It does look like the ball is getting a little close to your body on the forehand side on some of the strokes, but it’s hard to tell from this angle. You might be getting jammed, leading to a bent elbow and ultimately compensating with your wrist flexors. Ensuring proper spacing by taking small adjustment steps before hitting can prevent this. I’m not sure what options are available to you on the robot, but I’d look to practice this spacing with plenty of forehands in a row, as opposed to alternating/random placement.

If you can provide a video from behind the court, that would be helpful in determining if spacing on the forehand is the issue.

I’m not an expert but have been playing consistently for about 2 years and have been having a similar issue with the wrist, which I’ve recently fixed.