fix: real-time companion unlocks, persist exploration endsAt, correct auto-prestige formula, and quest balance

Closes #191
Closes #205
Closes #206
Closes #212
Closes #214
Closes #216
Closes #224

apps/web/src/context/gameContext.tsx

@@ -22,6 +22,7 @@ import {
   type NumberFormat,
   type Quest,
   type TranscendenceResponse,
+  computeUnlockedCompanionIds,
   isStoryChapterUnlocked,
 } from "@elysium/types";
 import {
@@ -72,7 +73,6 @@ import { playSound } from "../utils/sound.js";
 
 const autoSaveIntervalMs = 30_000;
 const autoPrestigeThresholdBase = 1_000_000;
-const autoPrestigeThresholdScale = 5;
 
 /**
  * Pure function — applies a boss challenge result to the game state.
@@ -1119,6 +1119,57 @@ export const GameProvider = ({
     });
   }, [ state ]);
 
+  // Detect newly unlocked companions whenever relevant state changes
+  useEffect(() => {
+    if (state === null) {
+      return;
+    }
+
+    const computedUnlocks = computeUnlockedCompanionIds({
+      apotheosisCount:         state.apotheosis?.count ?? 0,
+      lifetimeBossesDefeated:  state.player.lifetimeBossesDefeated,
+      lifetimeGoldEarned:      state.player.lifetimeGoldEarned,
+      lifetimeQuestsCompleted: state.player.lifetimeQuestsCompleted,
+      prestigeCount:           state.prestige.count,
+      transcendenceCount:      state.transcendence?.count ?? 0,
+    });
+
+    const currentUnlocks = state.companions?.unlockedCompanionIds ?? [];
+    const toAdd = computedUnlocks.filter((id) => {
+      return !currentUnlocks.includes(id);
+    });
+
+    if (toAdd.length === 0) {
+      return;
+    }
+
+    setState((previous) => {
+      if (previous === null) {
+        return previous;
+      }
+      const existingUnlocks = previous.companions?.unlockedCompanionIds ?? [];
+      const addedIds = computedUnlocks.filter((id) => {
+        return !existingUnlocks.includes(id);
+      });
+      if (addedIds.length === 0) {
+        return previous;
+      }
+      const updatedUnlocks = [ ...existingUnlocks, ...addedIds ];
+      const activeId = previous.companions?.activeCompanionId ?? null;
+      const validatedActiveId
+        = activeId !== null && updatedUnlocks.includes(activeId)
+          ? activeId
+          : null;
+      return {
+        ...previous,
+        companions: {
+          activeCompanionId:    validatedActiveId,
+          unlockedCompanionIds: updatedUnlocks,
+        },
+      };
+    });
+  }, [ state ]);
+
   // Game loop via requestAnimationFrame
 
   useEffect(() => {
@@ -1347,7 +1398,8 @@ export const GameProvider = ({
         && autoState.prestige.autoPrestigeEnabled === true
         && autoState.player.totalGoldEarned
           >= autoPrestigeThresholdBase
-            * Math.pow(autoPrestigeThresholdScale, autoState.prestige.count)
+            * Math.pow(autoState.prestige.count + 1, 2.5)
+            * (autoState.transcendence?.echoPrestigeThresholdMultiplier ?? 1)
       ) {
         isAutoPrestigingReference.current = true;
         void prestigeApi({}).