Groaning sound when accelerating?

Thank you for the video. It sounds like the transmission I would service the fluid and filter while taking note the condition of the old fluid. (Burnt?) Here is a guide to help walk you through the steps with instructions below to show you how on your car. It also could be a heat shield on the exhaust system, for this make sure the engine is cold then raise the car up and use a rubber mallet to gently bang on the exhaust system to see if you can duplicate the noise. The last thing I can think of is the serpentine belt tension, lift the hood to check it, I have left how to apply more tension on the belt in the images below.

Fluid type: .................... Toyota Genuine ATF D-II or DEXRON III (DEXRON II)

Capacities
Fluid capacity (drain and refill): .................... Up to 4.75 L (5.0 qt., 4.2 Imp.qt.)

https://www.2carpros.com/articles/how-to-service-an-automatic-transmission

Check out the images (below). Please let us know what happens.