Png transparency with opencv in python

Question

I've been using opencv to paste a png image over a background. My target is to simulate a sort of plastic bag underwater. In that way, I would like to apply Alpha in order to have the png image semi-transparent over the background, but when I do, the black mask of the png becomes transparent too.

y1, y2 = yoff, yoff + png.shape[0]
x1, x2 = xoff, xoff + png.shape[1]

alpha_png = png[:, :, 3] / 255.0
alpha_bg = 0.5 - alpha_png

bg_copy = bg.copy()

for c in range(0, 3):
    bg_copy[y1:y2, x1:x2, c] = (alpha_png * png[:, :, c] + alpha_bg * bg_copy[y1:y2, x1:x2, c])
cv2.imwrite("result.png", bg_copy)

I found this code online, and I changed the alpha_bg in order to make the image more or less transparent.

And the result is

I need to remove the black semi-transparent background, but the rest of the png should remain semi-transparent, plus the bag should get the background green color or underwater color (But I'll work later on this).

Any suggestion is really appreciated, also considering to use PIL instead of opencv.

Edit:

The used images are: Foreground

And Background:

Answer 1

Filling out the the details from the answer according Christoph Rackwitz, we crop the water image at the desired location to the size of the bag and blend with the bag image (bgr) using the mask from the alpha channel. Then we insert the resulting composite into a copy of the water image at the desired location.

import cv2
import numpy as np

# read the background image
water = cv2.imread('background.jpg')
h, w = water.shape[:2]
cx = w//2
cy = h//2

# read the foreground image
bag = cv2.imread('bag.png', cv2.IMREAD_UNCHANGED)
hh, ww = bag.shape[:2]

# separate bgr and alpha in bag image
bag_bgr = bag[:,:,0:3]
bag_alpha = bag[:,:,3]

# crop the water image at center to size of bag
water2 = water.copy()
water_crop = water2[cy:cy+hh, cx:cx+ww]

blend = 0.5
mask = blend*bag_alpha.astype(np.float32)/255
mask = mask[..., None]
composite = bag_bgr.astype(np.float32) * mask + water_crop.astype(np.float32) * (1-mask)
composite = composite.astype(np.uint8)

# insert composite into water
result = water.copy()
result[cy:cy+hh, cx:cx+ww] = composite

# save results
cv2.imwrite('water_bag2.jpg', result)

# show results
cv2.imshow('result', result)
cv2.waitKey(0)

Result: