Automatic transmission problem

Sounds like you have a major leak, and that can be good news. Without looking up the capacities, I can only guesstimate the transmission holds around nine to ten quarts of fluid, and with most external leaks you will lose about 3/4 of that. You will have to do the conversion to liters. Losing even 1/4 of the fluid is sufficient to cause the transmission to stop working.

Given your observation of a large puddle under the car, we can rule out things like a leaking pan gasket or output shaft seal. Those will leak very slowly over a long time. The hardest seal to replace that can leak suddenly and rapidly is the front pump seal between the engine and transmission. One of those has to be removed to change that seal. A more common suspect is a rubber hose going to the transmission cooler built into or in front of the radiator. You will have to look to see where the fluid is leaking from. If a large area is wet, watch where the fluid runs out when the engine is running. Do not run the engine longer than necessary because to lack of transmission fluid will stop some seals and bushings from being lubricated while parts are spinning. That can cause additional damage.

If someone needs to look up additional information, you will need to list the correct engine size. This model came with three versions of 3.0L V-6.

Those grooves are not normal wear, but it is doubtful they are the cause of this problem. Those would have developed gradually over time. Your transmission stopped working instantly. These grooves also will not cause fluid to leak onto the ground. If anything, it would make more sense an external leak occurred, then these grooves formed due to lack of lubrication caused by lack of fluid.