Safe-n-Sound is a rock based dense batt for use inside walls that is effective with little voc problems. https://www.rockwool.com/north-america/products-and-applications/products/safensound/
No VOC semi rigid panels with acoustacal holes. https://sonopan.com/?https%3A%2F%2Fsonopan_com%2F&gad=1&gclid=CjwKCAjw6IiiBhAOEiwALNqncVWq39gvCvyVENA7cg6UiqpqzQylGDmmbM8Ih9HNfntpAaXbqELlcBoCSxMQAvD_BwE
It is effective at sealing and cushioning panels. It never gets hard and requires off gassing. Best to avoid.
Acoustics is the proper term for the quality of sound inside a room, while soundproofing deals with reducing the passage of sound through walls. It is very difficult to stop all sound, but it can be significantly reduced. Most sound travels through air paths, so air sealing between two rooms is the first step. Many soundproofing and acoustical products have significant Volatile Organic Compound (VOC) off-gassing problems. Test everything.