Resolve persona prompts server-side; drop synthetic prompt in chat_turn

A request carrying persona_id but no system_prompt used to fall back to
the neutral default voice. Both agentic generation
(generate_agentic_insight_handler) and chat bootstrap now resolve the
persona's stored prompt from the persona store, with precedence:
explicit non-blank client system_prompt > persona store lookup >
existing default ("default" persona id behaves the same — used if the
store has a row, neutral default otherwise). Resolution happens at the
handler / bootstrap entry where the DAO is reachable; internals are
unchanged. resolve_bootstrap_system_prompt takes the resolved persona
prompt as a second argument, with precedence tests.

Also in insight_chat:

- Sync chat_turn no longer persists the synthetic "Please write your
  final answer now without calling any more tools." user message pushed
  on iteration exhaustion — extracted both streaming variants'
  synthetic_idx pattern into push/remove_synthetic_final_prompt (the
  remove is a defensive no-op on index drift) and applied it to all
  three loops; round-trip test included.
- Strip leaked <think> blocks from the final content persisted as the
  reply in chat_turn and both streaming AgenticLoopOutcomes (mid-stream
  TextDeltas are untouched; the raw transcript keeps the block).

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

src/ai/handlers.rs

@@ -809,6 +809,21 @@ pub async fn generate_agentic_insight_handler(
         .filter(|s| !s.trim().is_empty())
         .unwrap_or_else(|| "default".to_string());
 
+    // Server-side persona resolution: an explicit client `system_prompt`
+    // wins; otherwise the persona's stored prompt from the persona store;
+    // otherwise None and `build_system_content` applies its neutral
+    // default. Without the lookup, a request carrying only `persona_id`
+    // silently generated in the default voice.
+    let system_prompt = request
+        .system_prompt
+        .clone()
+        .filter(|s| !s.trim().is_empty())
+        .or_else(|| {
+            app_state
+                .insight_generator
+                .persona_system_prompt(user_id, &persona_id)
+        });
+
     let max_iterations: usize = std::env::var("AGENTIC_MAX_ITERATIONS")
         .ok()
         .and_then(|v| v.parse().ok())
@@ -834,7 +849,7 @@ pub async fn generate_agentic_insight_handler(
                 generator_for_task.generate_agentic_insight_for_photo(
                     &path_for_task,
                     request.model.clone(),
-                    request.system_prompt.clone(),
+                    system_prompt,
                     request.num_ctx,
                     request.temperature,
                     request.top_p,