Interesting you used the term hydrate because I only hear that used when talking about front-end web development (specifically Next and React) and it's a relatively new term. The "Hydration (web development)" Wikipedia article was only created in December 2020. https://en.wikipedia.org/wiki/Hydration_(web_development)
I feel like serialize/deserialize or marshal/demarshal are more common in broader computer science contexts.
"Hydrate" is much older than 2020. Here's a StackOverflow reference from 2011 [1], for instance. I first heard it used around that time, for loading objects from databases (in a banking context).
I feel like serialize/deserialize or marshal/demarshal are more common in broader computer science contexts.