No_Count_4807's journey

I recently had what I believe was the best interview of my career for a role at a prestigious institution. I felt incredibly prepared, established a great rapport with the interview team, and was completely confident that I would be a perfect fit for the position. After about two weeks, I received a call from their recruitment office informing me that I was in the finalist pool and they needed references. I had already arranged strong references ahead of time, so I reached out to them to submit their letters, which I confirmed were received through an email notification. However, it has now been three weeks since my references submitted their letters, and I haven't heard anything since. I'm starting to wonder if this long silence means they have chosen someone else. Is it typical to wait this long for an update, or should I reach out to inquire about the status of my application?