Make /ask free by default, Claude synthesis is opt-in

Search results (FTS5 + Ollama embeddings) are shown immediately at no
cost. AI synthesis via Claude is behind a "Synthesize" button that the
user must explicitly click. Results are cached permanently so repeat
visitors never trigger API calls.

- Split ask into search_only() (free) and ask() (paid, cached)
- GET /ask now uses search_only — no Claude tokens spent
- POST /api/ask/synthesize triggers Claude (Haiku, ~$0.001)
- Cached answers shown with "cached" badge, no re-generation
- Template shows sources immediately + optional synthesize button

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

src/webui/app.py

@@ -45,7 +45,8 @@ from webui.data import (
     get_author_network_full,
     get_citation_graph,
     get_comparison_data,
-    get_ask_data,
+    get_ask_search,
+    get_ask_synthesize,
     global_search,
 )
 
@@ -325,20 +326,32 @@ def ask_page():
     result = None
     if question:
         top_k = request.args.get("top", 5, type=int)
-        result = get_ask_data(db(), question, top_k=top_k)
+        # Search only (free) — returns sources + cached answer if available
+        result = get_ask_search(db(), question, top_k=top_k)
     return render_template("ask.html", question=question, result=result)
 
 
-@app.route("/api/ask", methods=["POST"])
-def api_ask():
-    """Answer a question via hybrid search + Claude. Returns JSON."""
+@app.route("/api/ask/synthesize", methods=["POST"])
+def api_ask_synthesize():
+    """Synthesize an answer via Claude (costs tokens, cached permanently). Returns JSON."""
     data = request.get_json(force=True, silent=True)
     if not data or "question" not in data:
         return jsonify({"error": "Missing 'question' in request body"}), 400
     question = data["question"]
     top_k = data.get("top_k", 5)
-    cheap = data.get("cheap", True)
-    result = get_ask_data(db(), question, top_k=top_k, cheap=cheap)
+    result = get_ask_synthesize(db(), question, top_k=top_k, cheap=True)
+    return jsonify(result)
+
+
+@app.route("/api/ask", methods=["POST"])
+def api_ask():
+    """Search only (free). Returns JSON with sources + cached answer if available."""
+    data = request.get_json(force=True, silent=True)
+    if not data or "question" not in data:
+        return jsonify({"error": "Missing 'question' in request body"}), 400
+    question = data["question"]
+    top_k = data.get("top_k", 5)
+    result = get_ask_search(db(), question, top_k=top_k)
     return jsonify(result)