fix(backend): stream DeerFlowClient AI text as token deltas (#1969)

DeerFlowClient.stream() subscribed to LangGraph stream_mode=["values",
"custom"] which only delivers full-state snapshots at graph-node
boundaries, so AI replies were dumped as a single messages-tuple event
per node instead of streaming token-by-token. `client.stream("hello")`
looked identical to `client.chat("hello")` — the bug reported in #1969.

Subscribe to "messages" mode as well, forward AIMessageChunk deltas as
messages-tuple events with delta semantics (consumers accumulate by id),
and dedup the values-snapshot path so it does not re-synthesize AI
text that was already streamed. Introduce a per-id usage_metadata
counter so the final AIMessage in the values snapshot and the final
"messages" chunk — which carry the same cumulative usage — are not
double-counted.

chat() now accumulates per-id deltas and returns the last message's
full accumulated text. Non-streaming mock sources (single event per id)
are a degenerate case of the same logic, keeping existing callers and
tests backward compatible.

Verified end-to-end against a real LLM: a 15-number count emits 35
messages-tuple events with BPE subword boundaries clearly visible
("eleven" -> "ele" / "ven", "twelve" -> "tw" / "elve"), 476ms across
the window, end-event usage matches the values-snapshot usage exactly
(not doubled). tests/test_client_live.py::TestLiveStreaming passes.

New unit tests:
- test_messages_mode_emits_token_deltas: 3 AIMessageChunks produce 3
  delta events with correct content/id/usage, values-snapshot does not
  duplicate, usage counted once.
- test_chat_accumulates_streamed_deltas: chat() rebuilds full text
  from deltas.
- test_messages_mode_tool_message: ToolMessage delivered via messages
  mode is not duplicated by the values-snapshot synthesis path.

The stream() docstring now documents why this client does not reuse
Gateway's run_agent() / StreamBridge pipeline (sync vs async, raw
LangChain objects vs serialized dicts, single caller vs HTTP fan-out).

Fixes #1969

backend/CLAUDE.md

@@ -395,11 +395,12 @@ Both can be modified at runtime via Gateway API endpoints or `DeerFlowClient` me
 **Architecture**: Imports the same `deerflow` modules that LangGraph Server and Gateway API use. Shares the same config files and data directories. No FastAPI dependency.
 
 **Agent Conversation** (replaces LangGraph Server):
-- `chat(message, thread_id)` — synchronous, returns final text
-- `stream(message, thread_id)` — yields `StreamEvent` aligned with LangGraph SSE protocol:
-  - `"values"` — full state snapshot (title, messages, artifacts)
-  - `"messages-tuple"` — per-message update (AI text, tool calls, tool results)
-  - `"end"` — stream finished
+- `chat(message, thread_id)` — synchronous, accumulates streaming deltas per message-id and returns the final AI text
+- `stream(message, thread_id)` — subscribes to LangGraph `stream_mode=["values", "messages", "custom"]` and yields `StreamEvent`:
+  - `"values"` — full state snapshot (title, messages, artifacts); AI text already delivered via `messages` mode is **not** re-synthesized here to avoid duplicate deliveries
+  - `"messages-tuple"` — per-chunk update: for AI text this is a **delta** (concat per `id` to rebuild the full message); tool calls and tool results are emitted once each
+  - `"custom"` — forwarded from `StreamWriter`
+  - `"end"` — stream finished (carries cumulative `usage` counted once per message id)
 - Agent created lazily via `create_agent()` + `_build_middlewares()`, same as `make_lead_agent`
 - Supports `checkpointer` parameter for state persistence across turns
 - `reset_agent()` forces agent recreation (e.g. after memory or skill changes)