Japan has opened its first osmotic power plant

Does it generate enough electricity from freshwater to offset the energy used to desalinate more water? Would it be more efficient to just treat the freshwater that would have been used to run the plant for drinking water and desalinate less water?

It seems like it would have to be more efficient to further treat the semi-treated wastewater. However there is often resistance to putting treated waste-water into reservoirs.

If you're using water at the end of a process that's just going to get mixed anyway, you're just extracting waste energy from the mixing process. Basically the fresh, used water and the highly saline water are in a lower-entropy state, and normally we'd just dump both in the ocean and allow the entropy to increase without extracting energy. But in this case we allow their entropy to increase in a controlled environment and so we're able to extract some energy in that process.

No, the fresh water always produces less energy than it took to desalinate the fresh water to begin with. If the freshwater is recoverable, that will always be energetically better. But if you can't recover the fresh water for some reason, like say there is a particular contaminant that is impractical to remove, or it's going to be used for some application like irrigation or feeding a nature preserve where higher salinity is tolerable but you're never getting the water back, then it reduces the overall system losses.

On the other hand, there are often restrictions on how concentrated your brine can be when released so it doesn't cause environmental problems. If you have to dilute your brine anyways, might as well get a little energy back.