The problem isn't that they need more padding, it's that their padding makes no sense. If they made a design decision to have tight padding that would be one thing, but they've got a horizontal layout with tight padding in the horizontal direction and wide padding in the vertical.
here's a really quick-and-dirty edit to even out the padding around each text block to be equal to the line height, which actually tightens up the total density by correcting the too-high line height in the notification text: https://imgur.com/uVcY6Sw