feat(bot): unified topic processor replacing router+interpreter stack

Replace 3-layer architecture (gpt-5-nano router + gpt-4o-mini interpreter) with
single unified topic processor (gpt-4o-mini) for simplified message handling.

New components:
- HouseholdContextCache: TTL-based caching (5 min) for household config data
- TopicProcessor: Unified classification + parsing with structured JSON output

Key changes:
- Renamed ASSISTANT_ROUTER_MODEL → TOPIC_PROCESSOR_MODEL
- Added TOPIC_PROCESSOR_TIMEOUT_MS (default 10s)
- Refactored save() → saveWithInterpretation() for pre-parsed interpretations
- Removed deprecated createOpenAiTopicMessageRouter and ~300 lines legacy code
- Fixed typing indicator to only start when needed (purchase routes)
- Fixed amount formatting: convert minor units to major for rawText

Routes: silent, chat_reply, purchase, purchase_clarification, payment,
payment_clarification, topic_helper, dismiss_workflow

All 212 bot tests pass. Typecheck, lint, format, build clean.

apps/bot/src/household-context-cache.ts

@@ -0,0 +1,48 @@
+import type { BotLocale } from './i18n'
+
+export interface CachedHouseholdContext {
+  householdContext: string | null
+  assistantTone: string | null
+  defaultCurrency: 'GEL' | 'USD'
+  locale: BotLocale
+  cachedAt: number
+}
+
+interface CacheEntry {
+  context: CachedHouseholdContext
+  expiresAt: number
+}
+
+export class HouseholdContextCache {
+  private cache = new Map<string, CacheEntry>()
+
+  constructor(private ttlMs: number = 5 * 60_000) {}
+
+  async get(
+    householdId: string,
+    loader: () => Promise<CachedHouseholdContext>
+  ): Promise<CachedHouseholdContext> {
+    const now = Date.now()
+    const entry = this.cache.get(householdId)
+
+    if (entry && entry.expiresAt > now) {
+      return entry.context
+    }
+
+    const context = await loader()
+    this.cache.set(householdId, {
+      context,
+      expiresAt: now + this.ttlMs
+    })
+
+    return context
+  }
+
+  invalidate(householdId: string): void {
+    this.cache.delete(householdId)
+  }
+
+  clear(): void {
+    this.cache.clear()
+  }
+}