feat: inspect the full prompt in the live log

The "context built" event now carries the fully-rendered prompt (persona, gists,
recalled details, recent turns, the new message) plus a total char count. The
log panel renders it as a collapsed "view full prompt" block — clean by default,
one click to see exactly what hit the model.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

lyra/chat.py

@@ -30,6 +30,11 @@ def _detail_note(exchanges: list[memory.Exchange]) -> Message:
     return {"role": "system", "content": body}
 
 
+def _render(messages: list[Message]) -> str:
+    """Human-readable dump of the exact prompt, for the live-log inspector."""
+    return "\n\n".join(f"[{m['role']}]\n{m['content']}" for m in messages)
+
+
 def build_messages(session_id: str, user_msg: str) -> list[Message]:
     """Assemble the full, tiered message list for one turn."""
     messages: list[Message] = [{"role": "system", "content": persona.system_prompt()}]
@@ -51,16 +56,17 @@ def build_messages(session_id: str, user_msg: str) -> list[Message]:
     if recalled:
         messages.append(_detail_note(recalled))
 
-    logbus.log(
-        "debug", "context built",
-        recent=len(recent), summaries=len(summaries), details=len(recalled),
-    )
-
     # Tier 3: current session, full fidelity.
     for ex in recent:
         messages.append({"role": ex.role, "content": ex.content})
 
     messages.append({"role": "user", "content": user_msg})
+
+    logbus.log(
+        "debug", "context built",
+        recent=len(recent), summaries=len(summaries), details=len(recalled),
+        chars=sum(len(m["content"]) for m in messages), detail=_render(messages),
+    )
     return messages