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/api/src/data/transcendenceUpgrades.ts

@@ -0,0 +1,133 @@
+import type { TranscendenceUpgrade } from "@elysium/types";
+
+export const DEFAULT_TRANSCENDENCE_UPGRADES: TranscendenceUpgrade[] = [
+  // ── Income multipliers ──────────────────────────────────────────────────────
+  {
+    id: "echo_income_1",
+    name: "Whisper of Power",
+    description: "The echoes of past runs linger, amplifying your guild's income by 25%.",
+    category: "income",
+    cost: 5,
+    multiplier: 1.25,
+  },
+  {
+    id: "echo_income_2",
+    name: "Resonance",
+    description: "Your transcendent experience resonates through your guild, boosting income by 50%.",
+    category: "income",
+    cost: 10,
+    multiplier: 1.5,
+  },
+  {
+    id: "echo_income_3",
+    name: "Harmonic Surge",
+    description: "The harmony of multiple timelines surges through your guild, doubling its income.",
+    category: "income",
+    cost: 20,
+    multiplier: 2.0,
+  },
+  {
+    id: "echo_income_4",
+    name: "Ethereal Overflow",
+    description: "Ethereal energy overflows from your transcendence, tripling your guild's income.",
+    category: "income",
+    cost: 40,
+    multiplier: 3.0,
+  },
+  {
+    id: "echo_income_5",
+    name: "Infinite Chorus",
+    description: "The infinite chorus of every run you've ever played amplifies your guild fivefold.",
+    category: "income",
+    cost: 80,
+    multiplier: 5.0,
+  },
+
+  // ── Combat multipliers ──────────────────────────────────────────────────────
+  {
+    id: "echo_combat_1",
+    name: "Battle-Hardened",
+    description: "Memories of countless battles harden your adventurers, increasing party DPS by 25%.",
+    category: "combat",
+    cost: 5,
+    multiplier: 1.25,
+  },
+  {
+    id: "echo_combat_2",
+    name: "Veteran's Edge",
+    description: "Veterans of transcendence know how to fight smarter, boosting party DPS by 50%.",
+    category: "combat",
+    cost: 15,
+    multiplier: 1.5,
+  },
+  {
+    id: "echo_combat_3",
+    name: "Transcendent Warrior",
+    description: "Your warriors carry the strength of every fallen timeline, doubling party DPS.",
+    category: "combat",
+    cost: 35,
+    multiplier: 2.0,
+  },
+
+  // ── Prestige threshold reductions ──────────────────────────────────────────
+  {
+    id: "echo_prestige_threshold_1",
+    name: "Accelerated Path",
+    description: "Experience from past lives shortens the road to prestige — threshold reduced by 10%.",
+    category: "prestige_threshold",
+    cost: 8,
+    multiplier: 0.9,
+  },
+  {
+    id: "echo_prestige_threshold_2",
+    name: "Shortcut Through Time",
+    description: "You've walked this path so many times you know every shortcut — threshold reduced by 20%.",
+    category: "prestige_threshold",
+    cost: 20,
+    multiplier: 0.8,
+  },
+
+  // ── Prestige runestone multipliers ─────────────────────────────────────────
+  {
+    id: "echo_prestige_runestones_1",
+    name: "Runic Attunement",
+    description: "Transcendent insight attunes you to the runestones, earning 50% more per prestige.",
+    category: "prestige_runestones",
+    cost: 8,
+    multiplier: 1.5,
+  },
+  {
+    id: "echo_prestige_runestones_2",
+    name: "Master Runesmith",
+    description: "You have mastered the art of runestone crafting, doubling your prestige runestone yield.",
+    category: "prestige_runestones",
+    cost: 20,
+    multiplier: 2.0,
+  },
+
+  // ── Echo meta multipliers ───────────────────────────────────────────────────
+  {
+    id: "echo_meta_1",
+    name: "Resonant Awakening",
+    description: "Your transcendence resonates deeper, amplifying future echo yields by 25%.",
+    category: "echo_meta",
+    cost: 10,
+    multiplier: 1.25,
+  },
+  {
+    id: "echo_meta_2",
+    name: "Transcendent Loop",
+    description: "Each loop of existence makes the next more powerful — future echo yields +50%.",
+    category: "echo_meta",
+    cost: 25,
+    multiplier: 1.5,
+  },
+  {
+    id: "echo_meta_3",
+    name: "Infinite Spiral",
+    description: "You have mastered the infinite spiral of transcendence, doubling all future echo yields.",
+    category: "echo_meta",
+    cost: 50,
+    multiplier: 2.0,
+  },
+];