For this case you need an adaptive threshold. ADAPTIVE_THRESH_GAUSSIAN_C should give the best results. But you should perform experiments with the blocksize. I think your value 11 is too small. The larger the blocksize, the smoother your T(x,y) threshold will be, and the less noisy the output.

for block_size in range(15, 40, 6):
    print(f'Attempt {block_size=}')
    binarized_image = cv2.adaptiveThreshold(image, 255, 
          cv2.ADAPTIVE_THRESH_GAUSSIAN_C, cv2.THRESH_BINARY, block_size, 2)
    save_my_image(binarized_image,f'myimage{block_size}.png')

You can also experiment with the last parameter, C=2. This is added to the threshold (or subtracted?) so it represents the binary cut-off. Using larger C will reduce the noise, but it may also remove details from the script.

After you find the best block_size, then run another experiment to find the best C value.