Transaxle

Most likely an engine mount was overlooked. GM engines commonly use a "dog bone" mount between the front top of the engine to the core support, just to the passenger side of the radiator. That is what keeps the engine from rocking. If that was not on your engine, the next most common location is underneath and to the rear of the engine. The link would go from the engine to the cross member.

When that link is missing or disconnected, when you shift to "park", and open the hood, you will see the engine rock back and forth excessively when you push the car forward or backward.

The clue is the rocking engine. That's controlled by the mounts. The only other factor is if idle speed is too high.

The torque converter clutch begins to lock up around 35 - 40 mph, when in the highest gears, and the engine is warmed up. Nothing related to it is engaged when the car is standing still. GM did have a big problem with that in the '80s. They wouldn't unlock as the car slowed, and it caused the engine to stall. Once stalled, it would release and allow the engine to be restarted. A lot of people "solved" that by unplugging the electrical connector for that solenoid, but that reduced fuel mileage.