NAC at the supplement dosage is generally considered to be safe, may reduce mucus production and inflammation. This article was published about 2 years ago, there is at least one on-going study:
https://bronchiectasisnewstoday.com/2019/05/09/n-acetylcysteine-potentially-beneficial-bronchiectasis-patients/
I have been using it for about 2 months, my mucus is a little less, and I think my ability to take deep breaths slowly is improving (used to be when I inhaled deeply my husband thought I was in distress - it's feeling better to me.)

As for post-nasal drip, it is generally related to the sinuses - mine was improved by surgery to repair the septum, remove polyps and stop an ever-present infection. I still must avoid certain things which cause it to worsen - exposure to pollens, mold and cats, tomato-paste/ketchup in large quantity, wheat...
Sue