In the absence of INDISPUTABLE EVIDENCE OF SPECIFIC GODS, DEISM is functionally identical to ATHEISM.

True but irrelevant to this hypothetical situation.

And even iff some sort of gods showed up, we'd really have to take-them-at-their-word.

Hypothetical situation. They have 'proven' that they have created you. Whatever you require as proof. So there would be no doubt that you were created by them for a specific function.

What would you tell your car if it asked you "why was I made?"

Good question. Would you tell it the truth?
Did you program 'Feelings' into the car?
Perhaps, since the question would pertain to curiosity, which would point to probable empathy, and also ability to ponder.
I would probably reprogram the car to eliminate the code that fostered the question....Unless that car was showing signs of 'will to live'.
If the car was created to transport me, then why would I create a curious AI? I would not, so this scenario would be very unlikely. Someone at Disney already thought up Sentient Cars ;)

What if a child asked their parent, "why did you make me?"

Why not the truth? -> Because I wanted to procreate, as I was designed to do.

By all appearances, we're some sort of experiment that was abandoned, and the results of the test long forgotten.

This is simply your Opinion, which I tend to think will change with time based on the rugs you choose to peek under now. You will be forced to logically deduce what Tesla and others have......That we will make more strides in science in a decade than we have in centuries once we embrace the study of that which cannot be seen... or something like that. Too tired to look up the quote.