The Report

At the end of the adventure comes a report: how many quests are done, open and failed, and Kira's gold, with the rewards from the done quests added.

For counting, you need a number for every status: an object with one key per status, which is what Record from the lesson on modeling data is for. And you don't have to write the statuses again: Quest["status"] from the previous lesson is the union of all of them. For example, monsters in a cave, counted by their kind:

type Monster = { kind: "goblin" | "wolf" | "troll"; name: string };

const cave: Monster[] = [
    { kind: "goblin", name: "Grub" },
    { kind: "wolf", name: "Grey" },
    { kind: "goblin", name: "Snag" },
];

const counts: Record<Monster["kind"], number> = { goblin: 0, wolf: 0, troll: 0 };
for (const monster of cave) {
    counts[monster.kind]++;
}
console.log(counts);
console.log(`Goblins: ${counts.goblin}`);

This prints:

{ goblin: 2, wolf: 1, troll: 0 }
Goblins: 2

counts[monster.kind] uses the kind as the key, so each monster adds one to its own count. TypeScript checks that the object has every key. In your program, without failed: 0, you'd get main.ts(122,7): error TS2741: Property 'failed' is missing in type '{ open: number; done: number; }' but required in type 'Record<"done" | "failed" | "open", number>'. And if a new status is ever added to Quest, TypeScript reports this object too.

Now the gold. Only a done quest has a reward, so reading quest.reward without a check is an error:

main.ts(126,35): error TS2339: Property 'reward' does not exist on type 'Quest'.
  Property 'reward' does not exist on type '{ status: "open"; title: string; }'.

Inside if (quest.status === "done"), TypeScript narrows the quest to a done one, and quest.reward is fine. Kira is in a const, but you can still change her gold: const only means that the variable always holds the same object.