dual pane side window shattered

The velocity of whatever hit it is not relevant other than something hit it hard enough to shatter it. It's tempered glass so if it breaks that's how it will break no matter what. You can use a center punch to easily break tempered glass and it's only a spring doing it. So although it may have been your neighbor's pellet gun, the fact that it shattered like that doesn't prove it. However, if it only broke one pain and not the other, and if it was the pellet gun, then there should be a pellet either stuck in the glass or laying on the ground close by.

If it were me I'd remove the broken glass and if you have to go without replacing it you probably can, but don't get into any rain. I would think water may be able to get inside your wall without the outter pain of glass there.