feat: initial elysium idle game prototype

Sets up the full monorepo with pnpm workspaces. Includes shared types
package, Hono API with Discord OAuth/JWT auth, Prisma v6 + MongoDB
Atlas, and React + Vite frontend with game loop, five tabs, and
Discord-linked save/load.

apps/web/src/engine/tick.ts

@@ -0,0 +1,96 @@
+import type { GameState } from "@elysium/types";
+
+/**
+ * Pure function — applies one game tick to the state.
+ * deltaSeconds: time elapsed since last tick.
+ * Returns a new GameState (does not mutate the original).
+ */
+export const applyTick = (state: GameState, deltaSeconds: number): GameState => {
+  let goldGained = 0;
+  let essenceGained = 0;
+
+  for (const adventurer of state.adventurers) {
+    if (!adventurer.unlocked || adventurer.count === 0) {
+      continue;
+    }
+
+    const upgradeMultiplier = state.upgrades
+      .filter(
+        (u) =>
+          u.purchased &&
+          (u.target === "global" ||
+            (u.target === "adventurer" && u.adventurerId === adventurer.id)),
+      )
+      .reduce((mult, upgrade) => mult * upgrade.multiplier, 1);
+
+    const prestige = state.prestige.productionMultiplier;
+
+    goldGained +=
+      adventurer.goldPerSecond * adventurer.count * upgradeMultiplier * prestige * deltaSeconds;
+
+    essenceGained +=
+      adventurer.essencePerSecond *
+      adventurer.count *
+      upgradeMultiplier *
+      prestige *
+      deltaSeconds;
+  }
+
+  // Complete active quests
+  const now = Date.now();
+  let questGold = 0;
+  let questEssence = 0;
+  let questCrystals = 0;
+
+  const updatedQuests = state.quests.map((quest) => {
+    if (
+      quest.status !== "active" ||
+      quest.startedAt == null ||
+      now < quest.startedAt + quest.durationSeconds * 1000
+    ) {
+      return quest;
+    }
+
+    const completed = { ...quest, status: "completed" as const };
+    for (const reward of quest.rewards) {
+      if (reward.type === "gold" && reward.amount != null) {
+        questGold += reward.amount;
+      } else if (reward.type === "essence" && reward.amount != null) {
+        questEssence += reward.amount;
+      } else if (reward.type === "crystals" && reward.amount != null) {
+        questCrystals += reward.amount;
+      }
+    }
+    return completed;
+  });
+
+  const newGold = state.resources.gold + goldGained + questGold;
+  const newEssence = state.resources.essence + essenceGained + questEssence;
+
+  return {
+    ...state,
+    resources: {
+      ...state.resources,
+      gold: newGold,
+      essence: newEssence,
+      crystals: state.resources.crystals + questCrystals,
+    },
+    player: {
+      ...state.player,
+      totalGoldEarned: state.player.totalGoldEarned + goldGained + questGold,
+    },
+    quests: updatedQuests,
+    lastTickAt: now,
+  };
+};
+
+/**
+ * Calculates the effective click power, including upgrades.
+ */
+export const calculateClickPower = (state: GameState): number => {
+  const clickMultiplier = state.upgrades
+    .filter((u) => u.purchased && u.target === "click")
+    .reduce((mult, upgrade) => mult * upgrade.multiplier, 1);
+
+  return state.baseClickPower * clickMultiplier * state.prestige.productionMultiplier;
+};