When it rains, it puddles. Spilled salt cycles between wet and dry with humidity. Is this akin to a phase change?
What is this process called exactly? As far as I understand
&quot;deliquescence&quot; is a property and not a process. Does the exchange of
water between my pile of salt and the air have a specific terminology?
Something that would go along with terms like evaporation,
sublimation, condensation, etc.? Perhaps some mash-up of adsorption
and dissolution?

The property of salts to become wet as I mentioned in another post Scientific Reason for Salt Solution Gaining Volume is deliquescence. The corresponding verb is to deliquesce. It is a pretty old word. From OED (not open access):

To melt or become liquid by absorbing moisture from the air, as certain salts.
1756   C. Lucas Ess. Waters i. 14   They attract the humidity of the
air, and deliquesce, or run liquid.
1781   Philos. Trans. 1780 (Royal Soc.) 70 349   This
pot-ash..deliquesces a little in moist air.
1876   D. Page Adv. Text-bk. Geol. (ed. 6) xvi. 299   Pure chloride of
sodium is not liable to deliquesce.*

Regarding phase changes, there were many phases changes involved in that process. The water as gas became liquid. The solid NaCl phase become one phase with a liquid. Once it evaporated, you got the solid again.