Your blade is about 150 cm^3 of tungsten, roughly 3 kg. That's a lot of mass to heat up and maintain at 3000 K. The surface area of your sword is about 550 cm^2. More surface area will radiate away the energy faster requiring a large battery and also melting the user.
All that heat will be right near your face and hands making it possibly impossible to hold without bulky thermal protection. Even if you were, the chaos of combat might result in your arm being jostled and that 3000 C blade brushing against YOU.
And, as others have noted, it won't even work against armor.
Swords were not terribly effective on the battlefield. They required being in close combat which makes it more likely you'll get injured. They require lots of room to swing, which means your allies have to stay well away from you leaving you fighting isolated. Movies which depict battles as a mixed brawl of individual sword battles are fantasy. Victorious ancient and medieval armies fought in tight formations. An isolated warrior is a dead warrior.
Swords are the service pistol of melee combat. They were a backup weapon you use when you lose your main weapon. Or used for duels.
If the sword wasn't your main weapon, what was? The polearm. And the ultimate expression of the polearm was the pike.
What you want is a heated pike. And you want a lot of them. And you probably want to scale it back to 1000 C.
Only heat the tip. It's much less mass to heat up and much smaller surface area to radiate that heat away meaning a smaller battery and potentially more pikemen. Add a bit of very high temperature insulation between the hot tip and the pole. The pole itself could be wood, good insulation, or perhaps aluminum. To protect the wiring from the battery to the tip, run it inside protected channel in the pole, or perhaps make the pole hollow. Having the heated tip at the end of a long pole keeps it well away from the user avoiding baking the user or their buddies next to them on the line.
Expecting to repeatedly bash anything at 3000 C against other things and expect to have anything but a lump of hot slag left over is ambitious. Scale it back to a mere 1000 C. Use a superalloy designed to hold together at that temperature. They will also be stronger, lighter, and sharper than tungsten. At the end of a pole you'll appreciate the reduced weight.
Thrusting with a sharp, light 1000 C alloy tipped pike is more likely to penetrate armor than slashing with a heavy, dull tungsten sword. Even if it doesn't penetrate it still scare the hell out of the enemy line.
Ancient and medieval warfare was a lot less stabbing and a lot more pushing, "the awful push of pike", with the goal of disrupting the enemy's formation. Even if you don't penetrate their armor, the enemy isn't going to want to confront a wall of lava-hot pikes. They will probably attempt to back away disrupting their formation and giving you victory.
Like this, but also on fire.