Phase 22: SearXNG web research pipeline + settings layout overhaul

Research pipeline (research_topic tool):
- New service: services/research.py — sub-query generation, SearXNG
  search, URL fetch, deduplication, and LLM synthesis into a note
- 5 sub-queries × 3 pages = up to 15 sources, capped at 12 for synthesis
- Synthesis uses num_ctx=16384 + max_tokens=8192 for long-form output
- Prompt demands 2500+ words, 6+ topic-appropriate sections, detailed prose
- 429 retry with backoff; 1s inter-query sleep; raw_decode JSON parsing

search_web tool (new):
- Lightweight single-query SearXNG search, results returned inline in chat
- LLM answers conversationally in round 1; no note created
- web_search result type with external links in ToolCallCard

Infrastructure:
- llm.py: generate_completion accepts num_ctx override
- config.py: SEARXNG_URL + Config.searxng_enabled()
- docker-compose: OLLAMA_NUM_PARALLEL=2, commented SEARXNG_URL example
- intent.py: search_web and research_topic routing rules

Settings UI:
- 2-column grid layout (small sections pair up, complex span full width)
- Search Test section: live SearXNG query with result preview
- GET /api/settings/search?q= proxy endpoint
- Research button (magnifier) in ChatView input toolbar → popover modal

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

src/fabledassistant/services/generation_task.py

@@ -28,6 +28,7 @@ from fabledassistant.services.intent import IntentResult, classify_intent
 from fabledassistant.services.logging import log_generation
 from fabledassistant.services.settings import get_setting
 from fabledassistant.services.tools import get_tools_for_user, execute_tool
+from fabledassistant.services.research import run_research_pipeline
 
 logger = logging.getLogger(__name__)
 
@@ -59,6 +60,8 @@ _TOOL_LABELS: dict[str, str] = {
     "update_todo": "Updating todo",
     "complete_todo": "Completing todo",
     "delete_todo": "Removing todo",
+    "search_web": "Searching the web",
+    "research_topic": "Researching topic",
 }
 
 # Tools that write data and require explicit user confirmation before executing.
@@ -285,6 +288,43 @@ async def run_generation(
                         if timing["ttft_ms"] is None:
                             timing["ttft_ms"] = int((time.monotonic() - t_start) * 1000)
 
+                    if tool_name == "research_topic":
+                        topic = intent.arguments.get("topic", "")
+                        if not ack_text:
+                            fallback_ack = f"I'll research '{topic}' and compile a note.\n\n"
+                            buf.append_event("chunk", {"chunk": fallback_ack})
+                            buf.content_so_far += fallback_ack
+                            if timing["ttft_ms"] is None:
+                                timing["ttft_ms"] = int((time.monotonic() - t_start) * 1000)
+                        try:
+                            note = await run_research_pipeline(
+                                topic, user_id, model, intent_model, buf
+                            )
+                            done_text = (
+                                f"Research complete! I've compiled a note: "
+                                f"**[{note.title}](/notes/{note.id})**."
+                            )
+                            buf.append_event("chunk", {"chunk": done_text})
+                            buf.content_so_far += done_text
+                            tool_record = {
+                                "function": "research_topic",
+                                "arguments": {"topic": topic},
+                                "result": {
+                                    "success": True,
+                                    "type": "research_note",
+                                    "data": {"id": note.id, "title": note.title},
+                                },
+                                "status": "success",
+                            }
+                            all_tool_calls.append(tool_record)
+                            buf.append_event("tool_call", {"tool_call": tool_record})
+                        except Exception as e:
+                            logger.exception("Research pipeline failed for topic: %s", topic)
+                            err_text = f"\nResearch failed: {e}"
+                            buf.append_event("chunk", {"chunk": err_text})
+                            buf.content_so_far += err_text
+                        break  # research IS the full response
+
                     confirmed = True
                     if tool_name in _WRITE_TOOLS:
                         loop = asyncio.get_running_loop()