Here, this should solve the issues you were experiencing.
import { world } from "@minecraft/server";
// Gets scoreboard objective. If undefined, adds it so it can be used.
const scoreboardKillstreak = world.scoreboard.getObjective("killstreak") ?? world.scoreboard.addObjective("killstreak", "killstreak");
world.afterEvents.entityDie.subscribe(evd => {
const { deadEntity, damageSource } = evd;
// This returns if deadEntity isn't a player, or the damageSource entity is undefined.
if (deadEntity.typeId !== "minecraft:player" || !damageSource.damagingEntity) return;
const player = damageSource.damagingEntity;
scoreboardKillstreak.addScore(player, 1);
const playerKS = scoreboardKillstreak.getScore(player);
world.sendMessage(`${player.nameTag} now has a §¶§c§lkillstreak§r§f of ${playerKS}!`);
});