I would say the simplest thing would be to state that Leia/the Resistance is aware that the First Order is up to something, maybe even building something, and they’re either trying to find evidence of what it is to convince the Republic to take action. Maybe they think finding Luke will help rally the Republic to their cause.

And yeah, maybe you could have Poe/Kylo hear Leia say something like, “Find their weapon”, taking it from “I was foolish to think I could find Luke…” and “The First Order, charging their weapon again now”. Or, she could just say, “The First Order weapon”. You could have someone record a generic Resistance officer say something like, “The First Order, they’re building something.”