feat: page interactive, démos Play/Step et simulateur Carnot

Ajoute le pipeline PageSpec (validation, rendu, publication /p/{slug}),
les démos TipTap /demo, et le simulateur Carnot (modes frigo/PAC/moteur,
énergie kJ vs puissance W, unités K/°C/°F) avec correctifs d’équations KaTeX.

Co-authored-by: Cursor <cursoragent@cursor.com>

memento-note/lib/ai/services/interactive-demo-client.service.ts

@@ -0,0 +1,74 @@
+import type { InteractiveDemoV1, ValidationIssue } from '@/lib/interactive-demo'
+
+export type GenerateInteractiveDemoResponse =
+  | { ok: true; demo: InteractiveDemoV1; attempts: number }
+  | {
+      ok: false
+      error: string
+      issues?: ValidationIssue[]
+      quotaExceeded?: boolean
+      status?: number
+    }
+
+export async function generateInteractiveDemo(params: {
+  content: string
+  selection?: string | null
+  lang?: string
+  noteId?: string
+}): Promise<GenerateInteractiveDemoResponse> {
+  const controller = new AbortController()
+  const timeout = setTimeout(() => controller.abort(), 170_000)
+  let res: Response
+  try {
+    res = await fetch('/api/ai/interactive-demo', {
+      method: 'POST',
+      headers: { 'Content-Type': 'application/json' },
+      body: JSON.stringify({
+        content: params.content,
+        selection: params.selection,
+        lang: params.lang,
+        noteId: params.noteId,
+      }),
+      signal: controller.signal,
+    })
+  } catch (err) {
+    clearTimeout(timeout)
+    const aborted = err instanceof Error && err.name === 'AbortError'
+    return {
+      ok: false,
+      error: aborted
+        ? 'Génération trop longue — réessaie (ou raccourcis la note)'
+        : err instanceof Error
+          ? err.message
+          : 'Network error',
+    }
+  } finally {
+    clearTimeout(timeout)
+  }
+
+  const data = await res.json().catch(() => ({}))
+
+  if (res.status === 402) {
+    return {
+      ok: false,
+      error: data.error || 'Quota exceeded',
+      quotaExceeded: true,
+      status: 402,
+    }
+  }
+
+  if (!res.ok) {
+    return {
+      ok: false,
+      error: data.error || `HTTP ${res.status}`,
+      issues: data.issues,
+      status: res.status,
+    }
+  }
+
+  return {
+    ok: true,
+    demo: data.demo,
+    attempts: data.attempts ?? 1,
+  }
+}