I was a real katana sicko in Elden Ring's base game, rocking Moonveil with an offhand Uchigatana from Caelid all the way through Ashen Leyndell. While there aren't many katanas in Shadow of the Erdtree, one of them is a new favorite weapon for me. Spoilers ahead about this weapon, and area details through the middle of the expansion.
Shadow of the Erdtree best katana stats and moveset
The Star-Lined Sword is an absolutely sick magic-focused katana with glowing Tron lines and one of my favorite Ashes of War, a slashing combo that injects Artorias-style acrobatics into a three-part attack reminiscent of Rivers of Blood. It's the same weapon used by the optional boss, Demi Human Swordsman Onze.
The Star-Lined Sword has B scaling in Dex, D Intelligence, and D Strength. I've found that it's not quite a straight upgrade on Moonveil's Transient Moonlight—though patch 1.12's nerf may have changed that. The Star-Lined Sword has similar damage at 60 Int, 60 Dex, though it may overtake Moonveil once you start investing in Strength.
In addition to just being rad as all hell, the Ash of War Onze's Line of Stars is situationally superior to Transient Moonlight. Transient Moonlight wins out as a way to quickly and safely damage bosses, while Onze's Line of Stars is well-suited for NPC foes, groups of enemies, or dangerous but relatively low-poise opponents like Cleanrot Knights.
Where to find the best katana in Shadow of the Erdtree
It's a bit of a trek to get the Star-Lined Sword, but it can be done well before reaching the halfway point of the DLC. You'll need to unlock the second major area, Scadu Altus. While there is a back way in via a spirit spring to the east of the Gravesite Plain, I recommend progressing normally through the DLC by beating the Divine Beast Dancing Lion and Knight Rellana on a first playthrough.
Once you have the Scadu Altus map, you'll notice a triangular pool of water next to a waterfall southeast of the Shadow Keep. There's a cave at the northern tip of that triangle that leads to a poison swamp. This path is long and circuitous, but linear—follow it until you reach the Ancient Ruins Base site of grace.
Follow this canyon to the west—you should find the map of this region on the way—and keep going until you dead end at the Temple Town Ruins in a large, shallow lake. There is a gravestone ladder to the south of the ruins that you can climb down with Torrent into another canyon. Follow this canyon south, below the Gravesite Plain, until you reach the Cerulean Coast site of grace at the bottom tip of the Land of Shadow. You can go south of the site of grace and just run past the undead dragon who accosts you to grab a map of the region.
Travel west from the Cerulean Coast site of grace until you find a graveyard full of lightning wisps and those annoying cemetery shades from the base game. Look for a canyon entrance in the rock wall north of this area and enter it.
If you start running into Demi Humans, including a reprise of Belurat Gaol boss Onze, you're on the right track. Follow this canyon as it curves to the west until it opens to a sandy beach with a Demi Human Queen boss. She should be easier than either instance of Onze or really any other boss in the DLC, but the fight is slightly complicated by the number of Demi Human minions around. Defeat her, and the Star-Lined Sword will be yours.