Another MIT paper on desalination from 2024 has a more conventional electrically powered system that can adjust its operating speed depending on how much power is coming in. So it can run off intermittent power sources such as its own solar panels.[3] Rather than buffering the energy with batteries, just buffer the water in a tank. This made it to field test and has some efficiency numbers.
It's annoying to see these one-off announcements with no followup. A short note a year later reporting why there's no further work would be useful to later workers.
[1] https://news.mit.edu/2023/desalination-system-could-produce-...
[2] https://drl.mit.edu/publications/journal/
[3] https://www.greenmemag.com/science-technology/breakthrough-m...
Obviously it needs to be cleaned regularly otherwise the salt encroaches into the sensitive bits. However the cleaning method doesn't require dissolving, just scraping.