Can confirm Discord requires a public-facing privacy policy at least for public bots. Can’t remember at what point I had to make one, but it is required for at least some cases.

“Public domain” is a copyright term which isn’t really relevant here. The point the other user is trying to make is that, legally speaking, calling something “private” when it very well may be not private is at best disingenuous and at worst a lawsuit waiting to happen.