Uranium has been extracted from seawater before. It's not economically practical, but it can be done, because seawater has uranium in it already. Tritium is also already in there.
Issues of concentration at the point where it is put into the ocean can be an issue, but once dispersed this won't turn the pristine, 0.0000000...% radioactive ocean into a radioactive hellscape, it represents an impercetible percentage increase of what is already there. That doesn't mean we shouldn't think about the implications, but "thinking about the implications" shouldn't start from incorrect understandings of the nature of the current world.
Earth is an amazing environment. It does an incredible job of giving us a low-radiation environment, compared to most of the rest of the universe which ranges from "dangerous" to "radioactive wasteland". But it's not perfect and we are not at a flat 0 even here.
And here is a good example of this in action. The optimal way to connect a nuclear power station to the grid is with a big overhead power line. Except that you would have to build it in a scenic area. Millions of people have a heuristic that make them believe thag powerlines damage the environment. There is no scientific basis for that. But you put the cable underground anyway at huge expense. The objective is to generate electricity, not deploy an absolutely optimal solution. And a piece of infrastructure built in the world has hundreds of issues like that. The only solution we have to that is politics.
Personally I don't disagree that nuclear is probably needed at least short term, but it's not a a reason to ignore or deny the problems it causes, some of them are hard to solve, and probably some also even hard to anticipate.