2019 Ford Edge water pump and powertrain

what does the water pump have to do with the power train on a 2019 ford edge ST and what may cause power train failures

I have trouble understanding what you are trying to ask . But it does not matter because if you have problems your vehicle is still in the warranty period.

Water pump is part of the engine, the engine is part of the power train.
If the water pump failed and you chose to continue to drive it while overheating, you cooked the engine. If this is the case, I would suspect, would not be covered by the warranty.