The sea is a big place. I could imagine perhaps some very localised effects near the plant, but even this isn't obvious.

> imagine > perhaps > but even this isn't obvious

So basically you're admitting you don't know anything about the subject, but you're making a conclusion anyway. It's OK to admit you don't know enough about a subject, and it's OK to not comment or theorize based on no knowledge besides an imagination.

A man once said, "imagination is more important than knowledge."

That man's name? Albert Einstein.

I didn’t know that making assumptions while clearly saying you are making assumptions is forbidden on HN.

Is the water cycle not a thing any more?

Not an expert but I could imagine some local negative effects. Salt concentration may get higher in the area where the brine is returned. Depending on volume, currents, etc...

A large part of the fresh water generated may be used for watering crops or gardens, and would thus evaporate in part. The evaporated water in desert areas would probably rain back down far way, and take long to mix with the sea near the plant again. For example, the Red Sea has much higher salinity that other oceans due to high evaporation and narrow connections to the other oceans. I doubt the effect is large though.

Indeed - the dead sea has stupid high salinity because the only way water leaves is via evaporation :)

It is a very odd sensation to "swim" in the dead sea. Even floating is pretty hard because you are so buoyant. It's probably the closes to true weightlessness I will ever get.