Since the hot fix, picking up a loot pack does nothing.
I think the ones you pick up during a game are auto-opened, since they’re shared across all players on the team? The ones you get for completing specific character challenges etc. remain unopened though, and appear in the Loot Packs tab.
You can get loot packs from chests or from challenges, in addition to just getting random loot itself. The loot packs tend to be on the rare side; I tend to only get a loot pack from a chest in about 25% of runs (most of said runs are Sentinel Advanced, and I know where all of the chests are, so that increases the chances).
And, yes, I have gotten loot packs like this since after the hot fix was applied.
When playing, if you open a chest and you see two of the loot pyramid things (I’m pretty sure a chest can’t have more than 1 piece of loot in it), one of them is going to be slightly bigger than the other; the slightly bigger one is a loot pack (since loot packs and loot are not the same thing).