I believe they use salts of other metals, not sodium. But in any case, in a salt the metal has already reacted with something and is unlikely to react further with commonly encountered substances.

Because a salt is an already-reacted substance. Molten sodium and molten sodium chloride are utterly different, for example.

https://onlinelibrary.wiley.com/doi/10.1002/cite.202000137

"In commercial CSP plants, almost exclusively a non-eutectic salt mixture of 60 wt % sodium nitrate and 40 wt % potassium nitrate is utilized. This mixture is commonly referred to as Solar Salt"

I've heard that salt has corrosion issues. These may also apply to sodium, though.

The Wikipedia article says that sodium actually protects metals from corroding, but I am unable to see how that works by reading the citation.

Some very reactive substances react with their container vessel to form a non-reactive 'skin' on the inside of the vessel. I don't know if they applies in this case.