The saving only exists if somebody negotiates it into the contract before the fact. Nothing in dual agency reduces the fee on its own.
Here's the mechanism. A listing agreement sets the total the seller pays their brokerage, say 5% on a 400k sale, which is 20k. Historically part of that got shared with whoever brought the buyer. If the listing agent brings the buyer themselves, the sharing step doesn't happen and the full 20k stays with one brokerage. The seller's obligation didn't change. That's why the number you see doesn't drop.
Some listing agreements do include a reduced rate for the case where the brokerage represents both sides, sometimes written as 5% normally and 4% if the firm procures the buyer. It has to be in the agreement in writing at signing. Asking for it afterward, once a buyer is standing there, is a much weaker position.
Since the NAR settlement, buyers sign their own written agreement with their agent stating that agent's compensation, and seller-paid buyer-side compensation is negotiated separately rather than assumed. So the two sides of the fee are more visible than they used to be, and a dual agency situation now has a paper trail showing exactly who's collecting what. Confirm the current forms and practice with the brokerage, because implementation differs by state and by firm.
One thing to hold onto as you figure out where you fit. The commission question and the representation question are separate. A discount on the fee doesn't buy back the advocate you gave up.