What do we do with this brine? Certainly not dumping it in the sea?
"Wastewater brine can pose a significant environmental hazard, both due to corrosive and sediment-forming effects of salts and toxicity of other chemicals diluted in it."
Seems like a well known problem with some solutions already in place
https://www.newscientist.com/article/2190929-growth-of-desal...
But I'm not sure the brine levels would actually be ever increasing.
Consider the water that we take out. Short term it goes somewhere on land to be used for some purpose humans deem useful to have land water for, but after that I'd guess that much of it eventually returns to the sea.
At some point wouldn't we reach a steady state where the rate we are taking water out to desalinate equals the rate that water from past desalination is returning?
At that point brine levels would be higher than before we started widespread desalination, but they would not longer be rising. As long as that new steady state higher brine level is not too high it might be OK.