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/tools.py

@@ -19,6 +19,7 @@ from fabledassistant.services.caldav import (
     update_event,
     update_todo,
 )
+from fabledassistant.config import Config
 from fabledassistant.services.notes import create_note, delete_note, get_note_by_title, list_notes, update_note
 from fabledassistant.services.tag_suggestions import suggest_tags
 
@@ -663,11 +664,61 @@ _CALDAV_TOOLS = [
 ]
 
 
+_SEARCH_TOOLS = [
+    {
+        "type": "function",
+        "function": {
+            "name": "search_web",
+            "description": (
+                "Search the web for quick information and answer the user's question from results. "
+                "Use for factual lookups, current events, version numbers, quick definitions, or any question "
+                "where a fast web answer is needed without creating a note. "
+                "Use research_topic instead when the user explicitly wants a comprehensive note or deep research."
+            ),
+            "parameters": {
+                "type": "object",
+                "properties": {
+                    "query": {"type": "string", "description": "The search query"}
+                },
+                "required": ["query"],
+            },
+        },
+    }
+]
+
+_RESEARCH_TOOLS = [
+    {
+        "type": "function",
+        "function": {
+            "name": "research_topic",
+            "description": (
+                "Research a topic by searching the web and compiling a note with cited sources. "
+                "Use for 'research X', 'look up X', 'find information about X', "
+                "'compile notes on X'. Takes 30–120 seconds."
+            ),
+            "parameters": {
+                "type": "object",
+                "properties": {
+                    "topic": {
+                        "type": "string",
+                        "description": "The topic or question to research",
+                    }
+                },
+                "required": ["topic"],
+            },
+        },
+    }
+]
+
+
 async def get_tools_for_user(user_id: int) -> list[dict]:
     """Build the tool list for a user based on their configured integrations."""
     tools = list(_CORE_TOOLS)
     if await is_caldav_configured(user_id):
         tools.extend(_CALDAV_TOOLS)
+    if Config.searxng_enabled():
+        tools.extend(_SEARCH_TOOLS)
+        tools.extend(_RESEARCH_TOOLS)
     logger.debug("User %d: %d tools available", user_id, len(tools))
     return tools
 
@@ -1128,6 +1179,32 @@ async def execute_tool(user_id: int, tool_name: str, arguments: dict) -> dict:
                 "data": {"id": note.id, "title": note.title},
             }
 
+        elif tool_name == "search_web":
+            from fabledassistant.services.research import _search_searxng
+            query = arguments.get("query", "")
+            results = await _search_searxng(query)
+            if not results:
+                return {"success": False, "error": f"No results found for '{query}'"}
+            return {
+                "success": True,
+                "type": "web_search",
+                "data": {
+                    "query": query,
+                    "results": results,
+                    "count": len(results),
+                },
+            }
+
+        elif tool_name == "research_topic":
+            # Research is always handled upstream in generation_task.py (round 0).
+            # This fallback exists in case it somehow reaches execute_tool.
+            topic = arguments.get("topic", "")
+            return {
+                "success": True,
+                "type": "research_pending",
+                "data": {"topic": topic},
+            }
+
         else:
             return {"success": False, "error": f"Unknown tool: {tool_name}"}