96 Toyota Camry rattles during acceleration

My 1996 Toyota Camry LE 4-cylinder recently started making what sounded like a hiss whenever I press the gas. The sound is clearly audible from the passenger side dashboard. It is accompanied by loss of engine power; the car does not accelerate at its normal speed. The sound occurs only when the car is in gear, not neutral/park. The car will stall if I press very lightly on the gas while it is moving slowly.

I jacked the front of the car up and placed it on jack stands so that the front wheels were off the ground. I was then able to take this video which illustrates that the sound is a clear rattle which grows into a spin as the engine speeds up. I thought the sound was coming from the EGR Vacuum Modulator, so I replaced it, and nothing changed.

Should I replace the EGR valve? Or is this something entirely different? Since my first attempt to diagnose the issue failed, I’d rather get more advice before I buy more parts.