I don’t recognize the sound specifically, but there are a number of components back there that deal with moving air.
There’s a hard vacuum line that runs under the fuel injectors on the driver-side cylinder bank, from a junction at the front of the head to a solenoid bolted at the back. This line gets brittle with age and can crack.
The thing you’re grabbing in the silver blanket in the video is the PCV valve.
Lower down behind the engine, there’s a secondary air injection pump. It’s more of a whirr and usually sounds like a jet engine when it fails. It’s also only active right after a cold start, for a brief period of time. If you have VCDS or a professional scan tool there’s an output test to manually activate it. It injects fresh air into the exhaust manifolds to help heat up the catalytic convertors more quickly.
It does this by feeding air to what are known as the “combi” valves, one for each head. These are opened by vacuum from the above-mentioned solenoid, and allow air from the SAI pump to pass to the manifolds.
The simplest way to check if it’s vacuum related would be to disconnect the lines from their source at the front of the intake manifold, on the left side when facing the engine bay. If the noise stops when the line is disconnected, you know you’ve got a problem with vacuum somewhere.
You could similarly try unplugging the SAI pump to prevent it from running, but be aware this will trigger the “check engine” light and set OBD II emissions codes in the ECU. Not a big deal if you’ve got a tool to reset codes, and it may take more than one cold start before it triggers.
Otherwise, you’ve got a standard collection of intake and emissions piping. A mechanic’s probe/stethoscope is cheap if you don’t have one and would help pinpoint the source of the sound.