The catalyst shortens the sprint time needed to trigger the Tesseract effect, which is described here (from https://gamerant.com/destiny-2-worldline-zero-exotic-sword/ ) : The Worldline Zero’s exotic perk is called Tesseract and although it sounds like something Thanos would be after, the perk actually lets the player teleport forward any time they use their heavy sword attack. Much like the light attack can help the player close short distances, this Tesseract attack will let them leap towards an enemy and deliver a substantial blow. It can be really nasty in Crucible.

That's a bit underwhelming considering the grind needed to get it.

Agreed. The 3 Exotic Swords from D1 Oryx expansion (RazeLight, Dark Drinker and BoltCaster if i remember names right) make any of the D2 swords look like blunt wooden sticks. The grind for them was bad, but the weapons were amazing to use. But Bungie doesn't really like swords anymore and it's going to be all about Bows going forward.

I remember those grinds. The only troublesome part about those old quests was the Alak-Hul strike at the end. Not just killing off the knights mind you, but just getting past that Shrieker room.

Yah. I and a group (all much lower than max light then) tried to do 3 swords at the same time on that phase. Didn't work out too well :) Wound up running it 3 times, but we got it done.