I've found that connections are off when playing on New Gen Consoles. But if I go back to play on Xbox One I don't have that issue. I feel as though I have to either suffer with 30fps and less smooth graphics and exponentially less lag or a Higher framerate with smoother graphics but significantly laggier lobbies.
I think it may have to do with framerate more than actual connection. I play on a Series S and perhaps that lag is because I'm playing against others on the Series X that have 120fps in Crucible as opposed to my 60fps.
Perhaps it is a server issue that can't properly handle the varying refresh rates at once.
I've had a plethora of odd things happen in crucible that absolutely makes no sense. Such as being killed behind walls, people not appearing on my radar to only appear right next to me, and shotgun me in the ass. But it doesn't seem to happen on the Xbox One. Only on new gen.
I don't know what you are playing on. But maybe that is the issue.
It's more, you're on next-gen (solo) you match against next-gen only and given how few next-gen console players there are in comparison to old gen.
Bungie in an effort to match players increased their tolerance for latency on next-gen. Which is probably why you experience lag to the extent you've seen of late.
That's just my take on what has been explained to me by more qualified people.