I noticed this as well during the livestream. I had thought they switched the camera shortly after that point, but watching through to landing it becomes clear that it's the same feed.
They did switch. I noticed differences during descent. In the last 10 seconds of descent, they became apparent, including the thrusters firing at different times and at edges of the screen, you could see orientation and direction of the two cameras were different.
The feed was that similar because the path of both boosters was this similar.