The other obvious product would be magnesium, but they didn't isolate magnesium chloride at the bromine plant. The Wylfa nuclear power station was nearby, and Rio Tinto had an aluminium smelter nearby to provide a base load. Since magnesium is oftentimes produced through electrolysis a magnesium plant would have made sense, but somehow they didn't build one, likely for economic reasons.
A 1GW nuclear power station consumes about 1t of U per year and produces about 8000GWh of electricity in that time. So we need about 1mg/8kWh. We got 12 times that much.
So, it sort of works out. Of course, this assumes a breeder reactor and I pretended that brine is purified uranium. If breeders are commercialized, it might be worth looking into this. Right now, it isn't.
This [1] article from 2012. It presents a Uranium extraction method from seawater that would put the extraction cost at $300/kg. Nowadays the market price is about $70/kg. However, if method were to be applied to brine instead of regular seawater, maybe the cost would go down. Hard to see it going down by a factor of 5 though.
Lithium from desalination brines seems to be one potential (and promising) such [0], environmentally better in more than one way than the current methods of lithium mining [1].
[0] https://www.researchgate.net/publication/313372304_Towards_l...
[1] https://www.wired.co.uk/article/lithium-batteries-environmen...