feat(costs): Pro-Nutzer-Kostenerfassung Stufe 1 (OpenRouter-Ist-Kosten)

CostMeter via ContextVars (app/core/costs.py, multitool-ready). Alle
OpenRouter-Calls (LLM, Sonar, Koreferenz, Fallback) senden usage:{include:true}
und buchen die Ist-Kosten je Kategorie (llm/web_search) — inkl. finalem
Streaming-usage-Chunk. cost_usage-Tabelle (user/day/category) + Store-Methoden;
ws.py/chat.py start_meter pro Turn + persist_costs. Statistik: Spalten
"Kosten (Monat)" + "Ø/Anfrage" + Gesamt. Live: 1 Such-Turn ~ $0,0052
(web_search dominiert, LLM ~ $0,00007). Tests: 318.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

app/tools/web_search.py

@@ -11,6 +11,7 @@ from dataclasses import dataclass, field
 
 import httpx
 
+from app.core.costs import record_openrouter_cost
 from app.metrics import metrics
 from app.providers.llm.base import lang_instruction
 
@@ -70,7 +71,8 @@ class SonarTool:
             logger.warning("SonarTool ohne API-Key")
             return ToolResult(text=_NO_DATA, ok=False)
 
-        payload = {"model": self.model, "messages": self._messages(query, language)}
+        payload = {"model": self.model, "messages": self._messages(query, language),
+                   "usage": {"include": True}}
         headers = {"Authorization": f"Bearer {self.api_key}", "Content-Type": "application/json"}
         timeout = httpx.Timeout(self.timeout)
 
@@ -90,6 +92,7 @@ class SonarTool:
                 return ToolResult(text=_NO_DATA, ok=False)
 
             data = resp.json()
+            record_openrouter_cost(data.get("usage"), "web_search")
             try:
                 content = data["choices"][0]["message"]["content"]
             except (KeyError, IndexError, TypeError):