feat(chat): integrate Langfuse tracing, prompt management & generation tracking

- shared/config.py: add LANGFUSE_SECRET_KEY, LANGFUSE_PUBLIC_KEY, LANGFUSE_HOST
- services/chat/app/tracing.py: new module — Langfuse client singleton,
  create_trace(), get_langfuse_callback(), get_prompt(), link_prompt_to_trace(),
  score_trace(), flush/shutdown helpers. Gracefully no-ops when keys are missing.
- services/chat/app/llm.py: add callbacks param to get_llm() for LangChain
  callback handler injection
- services/chat/app/deep_agent.py: accept langfuse_handler in all run_* and
  _run_single_agent* functions, pipe callbacks to LLM calls, fetch managed
  prompts from Langfuse with fallback to hardcoded system prompts
- services/chat/app/redis_consumer.py: create Langfuse trace per request
  (home_request/floating_request), pass callback handler to deep_agent,
  link prompt name to trace, attach output preview, flush after each request
- services/chat/app/main.py: shutdown Langfuse client in lifespan teardown
- services/chat/requirements.txt: add langfuse>=2.0.0

Langfuse prompt names: 'home_system', 'floating_system' — create these in
the Langfuse dashboard to manage prompts. Without them, hardcoded defaults
are used transparently.

services/chat/app/deep_agent.py

@@ -23,6 +23,7 @@ from app.agents.timeline_agent import TIMELINE_TOOLS
 from app.llm import get_llm
 from app.memory_middleware import MemoryMiddleware
 from app.ws_context import clear_tool_result_collector, execute_on_client, set_tool_result_collector
+from app import tracing
 from shared.db import async_session
 
 logger = logging.getLogger(__name__)
@@ -566,6 +567,19 @@ async def _infer_floating_domain(message: str, context: dict[str, Any]) -> dict[
     return _infer_floating_domain_rule_based(message, context)
 
 
+def _get_system_prompt(langfuse_name: str, fallback: str) -> str:
+    """Fetch a managed prompt from Langfuse, falling back to the hardcoded string."""
+    managed = tracing.get_prompt(langfuse_name, fallback=None)
+    return managed if managed is not None else fallback
+
+
+def _build_callbacks(langfuse_handler: Any | None) -> list[Any] | None:
+    """Return a callbacks list if a Langfuse handler is available."""
+    if langfuse_handler is None:
+        return None
+    return [langfuse_handler]
+
+
 async def _run_single_agent(
     *,
     user_id: str,
@@ -573,9 +587,11 @@ async def _run_single_agent(
     message: str,
     context: dict[str, Any],
     max_steps: int = 6,
+    langfuse_handler: Any | None = None,
 ) -> str:
     trace_id = _trace_id_from_context(context)
-    llm = get_llm()
+    callbacks = _build_callbacks(langfuse_handler)
+    llm = get_llm(callbacks=callbacks)
     tools = _all_tools_for_user(user_id, trace_id)
     model_context = _context_for_model(context)
     logger.info("deep_agent: run_single_agent_start trace=%s user=%s", trace_id or "-", user_id)
@@ -658,9 +674,11 @@ async def _run_single_agent_stream(
     message: str,
     context: dict[str, Any],
     max_steps: int = 6,
+    langfuse_handler: Any | None = None,
 ) -> AsyncGenerator[tuple[str, Any], None]:
     trace_id = _trace_id_from_context(context)
-    llm = get_llm()
+    callbacks = _build_callbacks(langfuse_handler)
+    llm = get_llm(callbacks=callbacks)
     tools = _all_tools_for_user(user_id, trace_id)
     model_context = _context_for_model(context)
     logger.info("deep_agent: run_single_agent_stream_start trace=%s user=%s", trace_id or "-", user_id)
@@ -751,25 +769,29 @@ async def _run_single_agent_stream(
         clear_tool_result_collector()
 
 
-async def run_home(user_id: str, message: str, context: dict[str, Any]) -> str:
+async def run_home(user_id: str, message: str, context: dict[str, Any], *, langfuse_handler: Any | None = None) -> str:
     prepared_context = await _prepare_context(message, context)
+    system_prompt = _get_system_prompt("home_system", _HOME_SINGLE_AGENT_SYSTEM)
     response = await _run_single_agent(
         user_id=user_id,
-        system_prompt=_HOME_SINGLE_AGENT_SYSTEM,
+        system_prompt=system_prompt,
         message=message,
         context=prepared_context,
+        langfuse_handler=langfuse_handler,
     )
     return _normalize_tagged_list_lines(response, message)
 
 
-async def run_floating(user_id: str, message: str, context: dict[str, Any]) -> tuple[str, dict[str, str | None]]:
+async def run_floating(user_id: str, message: str, context: dict[str, Any], *, langfuse_handler: Any | None = None) -> tuple[str, dict[str, str | None]]:
     prepared_context = await _prepare_context(message, context)
     domain = await _infer_floating_domain(message, prepared_context)
+    system_prompt = _get_system_prompt("floating_system", _FLOATING_SINGLE_AGENT_SYSTEM)
     response = await _run_single_agent(
         user_id=user_id,
-        system_prompt=_FLOATING_SINGLE_AGENT_SYSTEM,
+        system_prompt=system_prompt,
         message=message,
         context=prepared_context,
+        langfuse_handler=langfuse_handler,
     )
     sanitized = _strip_floating_markup(response)
     if not sanitized and response:
@@ -781,14 +803,18 @@ async def run_home_stream(
     user_id: str,
     message: str,
     context: dict[str, Any],
+    *,
+    langfuse_handler: Any | None = None,
 ) -> AsyncGenerator[tuple[str, Any], None]:
     prepared_context = await _prepare_context(message, context)
+    system_prompt = _get_system_prompt("home_system", _HOME_SINGLE_AGENT_SYSTEM)
     text_chunks: list[str] = []
     async for event in _run_single_agent_stream(
         user_id=user_id,
-        system_prompt=_HOME_SINGLE_AGENT_SYSTEM,
+        system_prompt=system_prompt,
         message=message,
         context=prepared_context,
+        langfuse_handler=langfuse_handler,
     ):
         event_type, data = event
         if event_type != "token":
@@ -805,19 +831,23 @@ async def run_floating_stream(
     user_id: str,
     message: str,
     context: dict[str, Any],
+    *,
+    langfuse_handler: Any | None = None,
 ) -> AsyncGenerator[tuple[str, Any], None]:
     prepared_context = await _prepare_context(message, context)
     domain = await _infer_floating_domain(message, prepared_context)
     yield "floating_domain", domain
 
+    system_prompt = _get_system_prompt("floating_system", _FLOATING_SINGLE_AGENT_SYSTEM)
     sanitizer = _FloatingStreamSanitizer()
     emitted_sanitized = False
     raw_chunks: list[str] = []
     async for event in _run_single_agent_stream(
         user_id=user_id,
-        system_prompt=_FLOATING_SINGLE_AGENT_SYSTEM,
+        system_prompt=system_prompt,
         message=message,
         context=prepared_context,
+        langfuse_handler=langfuse_handler,
     ):
         event_type, data = event
         if event_type != "token":