fix: resolve sync inflation, signature mismatch, CP accuracy, auto-buy cap, unlock hints

- #147: Guard all patch functions with hasChanged before incrementing
  sync counter to prevent inflation on no-op patches
- #148: Clear stale HMAC signature after each boss fight so subsequent
  auto-saves do not send a mismatched signature
- #146: Auto-unlock adventurer-specific upgrades in applyTick when
  their adventurer count > 0; show recruit hint in upgrade panel
- #149: Add Essence/s row to resource bar dropdown
- #150: Fix broken auto-quest CP reduce formula; centralise via
  computePartyCombatPower which applies all multipliers correctly
- #151: Cap auto-buy at 100 for non-max-tier adventurers; max tier
  (highest level unlocked) remains uncapped
- #152: Export computePartyCombatPower from tick, applying global
  upgrades, prestige, equipment, set bonuses, echo, crafted, and
  companion multipliers; use it in resource bar and boss panel

apps/web/src/engine/tick.ts

@@ -195,6 +195,138 @@ export const computeGoldPerSecond = (state: GameState): number => {
   return goldPerSecond;
 };
 
+/**
+ * Computes the current essence per second for the given game state,
+ * applying all relevant multipliers (upgrades, prestige, echo, crafted, companion).
+ * @param state - The current game state.
+ * @returns The total essence per second.
+ */
+export const computeEssencePerSecond = (state: GameState): number => {
+  const runestonesEssence = state.prestige.runestonesEssenceMultiplier ?? 1;
+  const craftedEssenceMultiplier
+    = state.exploration?.craftedEssenceMultiplier ?? 1;
+  const companionBonus = getActiveCompanionBonus(
+    state.companions?.activeCompanionId,
+    state.companions?.unlockedCompanionIds ?? [],
+  );
+  const companionEssenceMult
+    = companionBonus?.type === "essenceIncome"
+      ? 1 + companionBonus.value
+      : 1;
+
+  let essencePerSecond = 0;
+  for (const adventurer of state.adventurers) {
+    if (!adventurer.unlocked || adventurer.count === 0) {
+      continue;
+    }
+    const upgradeMultiplier = state.upgrades.
+      filter((upgrade) => {
+        const isGlobal = upgrade.target === "global";
+        const isThisAdventurer
+          = upgrade.target === "adventurer"
+          && upgrade.adventurerId === adventurer.id;
+        return upgrade.purchased && (isGlobal || isThisAdventurer);
+      }).
+      reduce((mult, upgrade) => {
+        return mult * upgrade.multiplier;
+      }, 1);
+    const contribution
+      = adventurer.essencePerSecond
+      * adventurer.count
+      * upgradeMultiplier
+      * state.prestige.productionMultiplier
+      * runestonesEssence
+      * craftedEssenceMultiplier
+      * companionEssenceMult;
+    essencePerSecond = essencePerSecond + contribution;
+  }
+  return essencePerSecond;
+};
+
+/**
+ * Computes the party's total combat power, applying all active multipliers
+ * (upgrades, prestige, equipment, set bonuses, echo, crafted, companion).
+ * This mirrors the server-side calculatePartyStats in boss.ts.
+ * @param state - The current game state.
+ * @returns The total party combat power.
+ */
+export const computePartyCombatPower = (state: GameState): number => {
+  let globalMultiplier = 1;
+  for (const upgrade of state.upgrades) {
+    if (upgrade.purchased && upgrade.target === "global") {
+      globalMultiplier = globalMultiplier * upgrade.multiplier;
+    }
+  }
+
+  // eslint-disable-next-line stylistic/no-mixed-operators -- prestige count * factor is clear
+  const prestigeMultiplier = 1 + state.prestige.count * 0.1;
+
+  const equipmentCombatMultiplier = state.equipment.
+    filter((item) => {
+      return item.equipped && item.bonus.combatMultiplier !== undefined;
+    }).
+    reduce((mult, item) => {
+      return mult * (item.bonus.combatMultiplier ?? 1);
+    }, 1);
+
+  const equippedItemIds = state.equipment.
+    filter((item) => {
+      return item.equipped;
+    }).
+    map((item) => {
+      return item.id;
+    });
+  const { combatMultiplier: setCombatMultiplier } = computeSetBonuses(
+    equippedItemIds,
+    EQUIPMENT_SETS,
+  );
+
+  const echoCombatMultiplier
+    = state.transcendence?.echoCombatMultiplier ?? 1;
+  const craftedCombatMultiplier
+    = state.exploration?.craftedCombatMultiplier ?? 1;
+
+  const companionBonus = getActiveCompanionBonus(
+    state.companions?.activeCompanionId,
+    state.companions?.unlockedCompanionIds ?? [],
+  );
+  const companionCombatMult
+    = companionBonus?.type === "bossDamage"
+      ? 1 + companionBonus.value
+      : 1;
+
+  let partyCombatPower = 0;
+  for (const adventurer of state.adventurers) {
+    if (adventurer.count === 0) {
+      continue;
+    }
+    let adventurerMultiplier = 1;
+    for (const upgrade of state.upgrades) {
+      if (
+        upgrade.purchased
+        && upgrade.target === "adventurer"
+        && upgrade.adventurerId === adventurer.id
+      ) {
+        adventurerMultiplier = adventurerMultiplier * upgrade.multiplier;
+      }
+    }
+    const contribution
+      = adventurer.combatPower
+        * adventurer.count
+        * adventurerMultiplier
+        * globalMultiplier
+        * prestigeMultiplier;
+    partyCombatPower = partyCombatPower + contribution;
+  }
+
+  return partyCombatPower
+    * equipmentCombatMultiplier
+    * setCombatMultiplier
+    * echoCombatMultiplier
+    * craftedCombatMultiplier
+    * companionCombatMult;
+};
+
 /**
  * Pure function — applies one game tick to the state.
  * DeltaSeconds: time elapsed since last tick.
@@ -469,6 +601,19 @@ export const applyTick = (
     challengeCrystals = result.crystalsAwarded;
   }
 
+  // Auto-unlock adventurer-specific upgrades when their adventurer is recruited
+  updatedUpgrades = updatedUpgrades.map((upgrade) => {
+    if (upgrade.unlocked || upgrade.adventurerId === undefined) {
+      return upgrade;
+    }
+    const adventurer = updatedAdventurers.find((a) => {
+      return a.id === upgrade.adventurerId;
+    });
+    return adventurer !== undefined && adventurer.count > 0
+      ? { ...upgrade, unlocked: true }
+      : upgrade;
+  });
+
   const goldValue = capResource(state.resources.gold + goldGained + questGold);
   const essenceValue = capResource(
     state.resources.essence + essenceGained + questEssence,