Salinity doesn't really work like that. You can't just dump a bunch of brine and expect it to just mix with the rest of the seawater. A lot of that depends on temperature, currents, etc. You might just end up forming a brine lake in the ocean if the brine just so happens to end up at the bottom without ever mixing. Not to mention brine isn't always just concentrated salt and water. It can include byproducts from desalination.
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Are there any brine reservoir in the ocean? That doesn't seem to be a thing. It either mixes properly with the ocean if proper mechanisms are set or it just ends up sinking to the bottom of the ocean and killing everything there.
There's storage inland, but that also has its own problems.
Nuclear waste in the ocean follows a similar idea (although larger in scope). You can't just dump it and be done. You have to create a plan to slowly release it (over decades) to (hopefully) not adversely affect life