OP, I have been in the same situation a few times, flying DL-ticketed, DL-coded flights on AM metal.
Note I never fly basic economy, and usually upgrade my Economy fare to a higher bucket to get some flexibility (note it is still an Economy fare, not Economy+).

My flight receipt from Delta has always said one free bag, but also always said this:

1/ If you qualify for free or discounted checked baggage, this will be taken into account when you check in.

but 2/ This trip is operated by Delta and the following carrier(s): . Visit delta.com for details on baggage embargoes that may apply to your itinerary. Also see other carrier's complete baggage information.

Point 1 seems to say that I will get a second free bag based on being STE+
Point 2 however, is trying to say what xliioper wrote above, which is that baggage policy of the operating carrier applies (note the text doesn't even mention the operating carrier)

The whole thing is highly misleading because it provides potentially conflicting info.

What I have always is complain to Delta after the fact using this link. I explain the situation, send the receipt of the AM baggage charge as well as a screen shot of the language on my ticket, and I have always been refunded the fee(s) in a few days. Once i even got a call from CS apologizing and giving me 2500 miles as a commercial gesture.

I would recommend you use the link (even better if you are logged in to DL.com before you click it, the system will offer you a list of your recent record locators to pick from and it speeds up the process).

Hopefully if a few of us do this, they will realize they need to clarify their wording, or policies with AM.

A.