feat: add transcendence second prestige layer

Implements the full Transcendence system — the ultimate endgame
mechanic, unlocked by defeating The Absolute One (requires Prestige 90).

Nuclear reset model: wipes resources, prestige, runestones, upgrades,
equipment, bosses, quests, zones, and achievements. Codex entries and
lifetime profile stats are preserved. Transcendence data is permanent
and accumulates across all future resets.

Echo formula: floor(853 / sqrt(prestigeCount)) × echoMetaMultiplier
Fewer prestiges = more Echoes, rewarding optimised play.

15 Echo upgrades across 5 categories:
- Income multipliers (×1.25 → ×5): 5 tiers, cost 5–80 echoes
- Combat multipliers (×1.25 → ×2): 3 tiers, cost 5–35 echoes
- Prestige threshold reductions (×0.9, ×0.8): cost 8–20 echoes
- Prestige runestone multipliers (×1.5, ×2): cost 8–20 echoes
- Echo meta multipliers (×1.25 → ×2): cost 10–50 echoes

New files: Transcendence.ts types, transcendence service, route,
data files (API + web), TranscendencePanel.tsx component.

Modified: GameState, Api, types/index, prestige service (carries
transcendence through resets, applies echo multipliers), boss route
(echoCombatMultiplier), game.ts anti-cheat (echo cap), tick.ts
(echoIncomeMultiplier), GameContext, API client, GameLayout (new tab),
ResourceBar (transcendence badge alongside prestige badge), styles.css,
AboutPanel, IDEAS.md.

apps/web/src/components/game/GameLayout.tsx

@@ -14,12 +14,13 @@ import { EditProfileModal } from "./EditProfileModal.js";
 import { EquipmentPanel } from "./EquipmentPanel.js";
 import { OfflineModal } from "./OfflineModal.js";
 import { PrestigePanel } from "./PrestigePanel.js";
+import { TranscendencePanel } from "./TranscendencePanel.js";
 import { QuestPanel } from "./QuestPanel.js";
 import { StatisticsPanel } from "./StatisticsPanel.js";
 import { UpgradePanel } from "./UpgradePanel.js";
 import { DailyChallengePanel } from "./DailyChallengePanel.js";
 
-type Tab = "adventurers" | "upgrades" | "quests" | "bosses" | "equipment" | "achievements" | "prestige" | "statistics" | "daily" | "codex" | "about";
+type Tab = "adventurers" | "upgrades" | "quests" | "bosses" | "equipment" | "achievements" | "prestige" | "transcendence" | "statistics" | "daily" | "codex" | "about";
 
 const BASE_TABS: { id: Tab; label: string }[] = [
   { id: "adventurers", label: "⚔️ Adventurers" },
@@ -29,6 +30,7 @@ const BASE_TABS: { id: Tab; label: string }[] = [
   { id: "equipment", label: "🗡️ Equipment" },
   { id: "achievements", label: "🏆 Achievements" },
   { id: "prestige", label: "⭐ Prestige" },
+  { id: "transcendence", label: "🌌 Transcendence" },
   { id: "statistics", label: "📊 Statistics" },
   { id: "daily", label: "📅 Daily" },
   { id: "codex", label: "📖 Codex" },
@@ -66,6 +68,7 @@ export const GameLayout = (): React.JSX.Element => {
         resources={state.resources}
         runestones={state.prestige.runestones}
         prestigeCount={state.prestige.count}
+        transcendenceCount={state.transcendence?.count ?? 0}
         profileUrl={profileUrl}
         onEditProfile={() => { setEditingProfile(true); }}
         lastSavedAt={lastSavedAt}
@@ -112,6 +115,7 @@ export const GameLayout = (): React.JSX.Element => {
             {activeTab === "equipment" && <EquipmentPanel />}
             {activeTab === "achievements" && <AchievementPanel />}
             {activeTab === "prestige" && <PrestigePanel />}
+            {activeTab === "transcendence" && <TranscendencePanel />}
             {activeTab === "statistics" && <StatisticsPanel />}
             {activeTab === "daily" && <DailyChallengePanel />}
             {activeTab === "codex" && <CodexPanel />}