one thing which you can do is capture a screenshot of that area using and extract the text later using tesseract. Got same issue as text entered is not being stored in value attribute
EG:
to capture screenshot
featureElement = browser.find_element_by_xpath("//textarea//..")
featureElement.screenshot('foo.png')
#to read from image
images = cv2.imread('image_path')
convert to grayscale image
gray = cv2.cvtColor(images, cv2.COLOR_BGR2GRAY)
cv2.threshold(gray, 0, 255, cv2.THRESH_BINARY | cv2.THRESH_OTSU)[1]
memory usage with image i.e. adding image to memory
filename = "{}.jpg".format(os.getpid())
cv2.imwrite(filename, gray)
text = pytesseract.image_to_string(Image.open(filename))
print(text)