How do I convert to camera pose in world from rvec and tvec of cv2.SolvePnP

Question

I'm trying to get quaternions and translations out of rvec and tvec with code like this:

import cv2
import numpy as np
from scipy.spatial.transform import Rotation
# 2d
image_points_2D = [[1331.284,610],[1473.253,468.6115], [1191.823,748.8911],[1473.253,751.3885],[1191.823,471.1088],[1245.413,347.5563],[1501.027,477.5027],[1487.591,610]]
# 3d
figure_points_3D =[[ 0. ,0., -0.5 ], [ 0.5, 0.5, -0.5 ],[-0.5,-0.5,-0.5 ],[ 0.5 , -0.5, -0.5 ],[-0.5 ,  0.5, -0.5 ],[-0.45,  1. ,  0.4 ],[ 0.5 ,  0.5,  0.5 ],[ 0.5 ,  0. ,  0.  ]]
# camera
distortion_coeffs = np.zeros((4,1))
matrix_camera = np.array([[flx, 0, center_x],
                          [0, fly, center_y],
                          [0, 0, 1         ]], dtype = "double")
# PnP
success, vector_rotation, vector_translation = cv2.solvePnP(figure_points_3D, image_points_2D, matrix_camera, distortion_coeffs, flags=cv2.SOLVEPNP_ITERATIVE)
# get loss
reprojected_points, _ = cv2.projectPoints(figure_points_3D, vector_rotation, vector_translation, matrix_camera, distortion_coeffs)
loss = np.mean(np.abs(image_points_2D - reprojected_points.reshape(image_points_2D.shape)))
print("loss", loss)

# get pose
rotation = Rotation.from_rotvec(vector_rotation.flatten())
print("quat (x,y,z,w): ", rotation.as_quat())
print("translation", vector_translation.flatten())

Here the Loss value is displayed as 0, so I think the rvec and tvec values are correct.

On Unity (Game Engine), the camera look the target at the origin position (0,0,0) on Unity from camera position (-2, 0, -15) and pose (XYZW: 0, -0.131, 0, 0.991). The value of tvec is correct. However, the quaternion that converted from the rvec values have their y and w components inverted. Why is this?

Expected quaternion (Unity): (XYZW: 0, -0.131, 0, 0.991)

Output quaternion (solvePnP): (XYZW: 0, -0.991, 0, 0.131)