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It's easier to understand with a picture of the process:
It's not energy negative. Osmosis doesn't require any energy input. You only need to pump water to the plant,but the harvested power from the pressurized water exceeds the required pumping power. Freshwater and saltwater are freely available. Using the concentrated brine from a desalination plant only increases the efficiency.
I mean the part in the picture is clear to me. But if we assume freshwater is freely available, why would they want to power a desalination plant with the generated power? Basically you can trade freshwater (or salinity gradient generally) for power or power for freshwater. But in a simple loop you'd only lose both over time due to inefficiency.
doesn't completely answer your question, but:
so it would seem it happens to be a net positive due to the energy "stored" in the brine
Hm from reading more on it, I think it has more to do with droughts in the area. That is why they build the desalination plant in the first place. I assume using the residual energy of the saline gradient (+ the boost from the brine) to generate new freshwater is better than further draining the naturally occuring freshwater. But still just a guess.