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I wrote my comment in response to the question, and IMO, I did it justice by listing the various considerations that would arise, in the order which seemed most logical to me. At no point did I believe I was writing a design manual for how to approach such a project.
There are much smarter people than me with far more sector-specific knowledge to "properly consider the problem" but if you expected a feasibility study from me, then I'm sorry to disappoint. My answer, quite frankly, barely arises to a back-of-the-envelope level, the sort of answer that I could give if asked the same question in an elevator car.
While the word California didn't show up in the question, it's hard to imagine a "state on the coast" with "excess solar" where desalination would be remotely beneficial. 30 US States have coastlines, but the Great Lakes region and the Eastern Seaboard are already humid and wet, with rivers and tributaries that aren't exactly in a drought condition. That leaves the three West Coast states, but Oregon and Washington are fairly well-supplied with water in the PNW. That kinda leaves California, unless we're talking about Mexican states.
I'm not dissing on the concept of desalination. But the literature for existing desalination plant around the world showcases the numerous challenges beyond just the money. Places like Israel and Saudi Arabia have desalination plants out of necessity, but the operational difficulties are substantial. Regular clogging of inlet pipes by sealife is a regular occurrence, disposal of the brine/salt extracted is ecologically tricky, energy costs, and more. And then to throw pumped hydro into this project would make it a substantial undertaking, as dams of any significant volume are always serious endeavors.
At this point, I feel the question is approaching pie-in-the-sky levels of applicability, so I'm not sure what else I can say.