fix(search): keep reasoning out of web search queries and stop misrouting named targets (#7054)

* fix(llm): keep reasoning out of answers when thinking is off

Small-budget utility calls on reasoning models spend every token on
reasoning, and llm_call then returned reasoning_content as the answer. Web
search extraction sent that text to SearXNG as the query, which found
nothing, and session titles fell back as unusable.

Treat thinking_mode="off" as "only the answer": non-streaming calls now
return empty instead of substituting reasoning, matching the streaming path.
Callers that do not turn thinking off keep the existing fallback.

Turn thinking off for search query extraction, session titles without a
configured effort, scheduled task names, and deep research classification,
and strip inline think blocks from the extracted query.

* fix(routing): require computer task wording for named hosts

"on <word>" and "from <word>" counted as a named computer on their own, so
"Who is Jensen Huang from NVIDIA?" and "What happened on Monday?" routed to
shell tools and the workspace toolset.

A target now only counts next to wording that describes work on a machine,
such as "check disk usage on gpu-box" or "copy the logs from gpu-box". The
intent classifier and the agent loop's local computer check share the pattern.

* fix(chat): resolve follow-up references in web search queries

Query extraction only saw the latest message, so "Does he work with Lisa
Su?" lost who "he" was. Include the last four turns, capped per turn, and
instruct the model to use them only to resolve references. Incognito turns
do not use saved session history.

* test(llm): stop reasoning fallback tests hanging in isolation

The module replaced src.agent_tools and core.database with MagicMock before
importing agent_loop. strip_tool_blocks then returned a mock, and
_strip_think_blocks looped forever because a mock's find() never returns -1.
This hung whenever the file ran alone or first on a worker. Import the real
modules instead.

* test(search): remove extra blank line at EOF

---------

Co-authored-by: Alexandre Teixeira <general@alexandreteixeira.dev>

tests/test_task_chain_owner_scope.py

@@ -17,6 +17,7 @@ clear_fake_database_modules()
 import core.database as cdb
 import routes.task_routes as task_routes
 from core.database import ScheduledTask
+from routes.task.task_routes import TaskCreate
 
 _TMPDB = tempfile.NamedTemporaryFile(suffix=".db", delete=False)
 _ENGINE = create_engine(
@@ -125,3 +126,32 @@ def test_scheduler_cycle_guard_treats_cross_owner_chain_as_unsafe():
         assert scheduler._has_chain_cycle(db, "bob-target-cycle", owner="alice") is True
     finally:
         db.close()
+
+
+@pytest.mark.asyncio
+async def test_generated_task_name_turns_thinking_off(monkeypatch):
+    sent = {}
+
+    async def fake_call(**kwargs):
+        sent.update(kwargs)
+        return "Daily AI News"
+
+    monkeypatch.setattr("src.llm_core.llm_call_async", fake_call)
+    db = _TS()
+    try:
+        db.add(cdb.Session(
+            id="task-name-session", name="s", owner="alice",
+            endpoint_url="http://127.0.0.1:8081/v1", model="gemma4-26b",
+        ))
+        db.commit()
+    finally:
+        db.close()
+    create_task = _endpoint("POST", "/api/tasks")
+    created = await create_task(
+        SimpleNamespace(state=SimpleNamespace(current_user="alice"), headers={}),
+        TaskCreate(prompt="Summarize AI news", task_type="llm", trigger_type="webhook"),
+    )
+
+    assert sent["thinking_mode"] == "off"
+    assert sent["max_tokens"] == 20
+    assert created["name"] == "Daily AI News"