Why do the protagonist seem to suddenly understand the people of Facade?

It's not so much that the protagninst learns to understand the people of Facade, it's Weiss who learns to understand them.

During your first visit Facade, the dialogue with residents lacks said parathesis you mentioned (indicating they are speaking, but you do not understand them). Weiss is amazed and comments on how they speak a language he has never encountered before. When you meet the young girl who speaks through (I guess sign language and interpretive dance), Weiss begins to slowly learn their language while speaking with her and taking the tour of Facade. Throughout this tour, Weiss takes a lot of pauses while translating their language back to you.

After the tour is complete is when the dialogue starts to readable, and the protagonist seems to somehow "understand" them. What is really happening is that Weiss learns their language and translate back to you real-time so ... you ... don't ... have .... to ... sit ... there ... waiting ... for ... the ... dialogue