The way I do it, each NPC's knowledge (or "working memory") gets saved, so they would retain "has seen the player recently". Then upon loading that file, their behavior tree will use that knowledge to get them back into the "is looking for them" state.
I experimented with saving the full behavior tree state once, but it massively bloated my save files, was very brittle (couldn't resolve the state if I changed the structure of behavior trees), and didn't really gain anything.