Decreasing levels of other channels when voice channel comes in I'm recording commentary over a video, and when I'm talking in the commentary I'd like the other channel's audio to get quieter to compensate for my voice. If anyone is familiar with discord, I know that when talking to people in a group chat it makes other programs quieter, if that helps make sense of what I'm trying to do.

I'm really inexperienced with video editing, but I have access to audacity, Adobe audition, and premiere. I'm also open to other programs (free or cheap) if they can do this easier.
"Ducking" is the canonical term for what you want, usually done with a compressor in the main program chain with the sidechain taken from your mic channel.  

Audition 2018 has a auto ducking feature that may be of use, but really anything that lets you drop an audio compressor across the program bus and sidechain it to the mic input will work.