Okay, that is not the transfer case module for sure. If you turn the car on without starting the engine, does it still make the noise, and thank you for the video, it helps. If it makes the noise with the engine running, we need to remove the serpentine belt and then start the engine (briefly) to see if the noise is still there, please upload another video is you can, also can you tell if the noise is coming from under the car or at the engine front? Here is how to remove the belt in the images below. This generic guide can help as well.
https://www.2carpros.com/articles/replace-serpentine-belt
Please get back to us so we can help you fix it or at least see what is wrong. It is a strange noise, nothing obvious. Also, with the engine off can you try to spin the radiator cooling fans (2) to see if they move freely? These can make noises as well.
Images (Click to make bigger)
Monday, February 13th, 2023 AT 1:35 PM