feat(chat): add AI memory panel with persistent facts (M9.7)

Collapsible memory panel below persona selector. Add/edit/delete
persistent facts (max 20) injected into every system prompt. Facts
stored in localStorage, shown as collapsed "Memory (N/20)" toggle.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

packages/app/src/composables/useAI.ts

@@ -4,6 +4,7 @@ import { searchWeb } from '@/composables/useWebSearch'
 import { getApiKey } from '@/utils/key-vault'
 import type { ImageAttachment } from '@aiui/core/types/message'
 import { usePersonaStore } from '@/stores/personas'
+import { useMemoryStore } from '@/stores/memory'
 
 type Provider = 'claude' | 'openrouter' | 'mock'
 
@@ -304,7 +305,7 @@ function formatWebSearchContext(results: { title: string; url: string; content?:
 - You MAY add [[podcast_ext:...]] or [[film_ext:...]] tags for "to learn more" recommendations after your answer.\n\n${lines.join('\n')}`
 }
 
-/** Build the system prompt, incorporating persona if active */
+/** Build the system prompt, incorporating persona and memory */
 function buildSystemPrompt(chatStore: ReturnType<typeof useChatStore>): string {
   let prompt = SYSTEM_PROMPT
 
@@ -318,6 +319,10 @@ function buildSystemPrompt(chatStore: ReturnType<typeof useChatStore>): string {
     }
   }
 
+  // Append memory facts
+  const memoryStore = useMemoryStore()
+  prompt += memoryStore.buildMemoryContext()
+
   if (chatStore.webSearchEnabled) {
     prompt += `