fix(desktop): keep live model switch metadata truthful

A live config.set model switch already moved the next API call to the new model,
but the conversation could still restore an old sessions.system_prompt snapshot
whose Model/Provider lines named the previous runtime. That made "what model are
you?" answer from stale metadata even while inference ran on the new model.

After a live switch we now refresh the stored system prompt and append a real
system-history pivot (not a fake user turn) so the transcript itself records the
new model/provider. Restore also rejects already-stale prompt snapshots when
their Model/Provider lines disagree with the runtime, so existing bad sessions
self-heal.

agent/conversation_loop.py

@@ -300,11 +300,20 @@ def _restore_or_build_system_prompt(agent, system_message, conversation_history)
                 agent.session_id, exc,
             )
 
-    if stored_prompt:
+    if stored_prompt and _stored_prompt_matches_runtime(agent, stored_prompt):
         # Continuing session — reuse the exact system prompt from the
         # previous turn so the Anthropic cache prefix matches.
         agent._cached_system_prompt = stored_prompt
         return
+    if stored_prompt:
+        stored_state = "stale_runtime"
+        logger.info(
+            "Stored system prompt for session %s has stale runtime identity; "
+            "rebuilding for model=%s provider=%s.",
+            agent.session_id,
+            getattr(agent, "model", "") or "",
+            getattr(agent, "provider", "") or "",
+        )
 
     if conversation_history and stored_state in ("null", "empty"):
         # Continuing session whose stored prompt is unusable.  The
@@ -366,6 +375,30 @@ def _restore_or_build_system_prompt(agent, system_message, conversation_history)
             )
 
 
+def _stored_prompt_matches_runtime(agent, prompt: str) -> bool:
+    """Return False when the persisted Model/Provider lines are stale."""
+
+    def line_value(label: str) -> str:
+        prefix = f"{label}:"
+        value = ""
+        for line in prompt.splitlines():
+            if line.startswith(prefix):
+                value = line[len(prefix):].strip()
+        return value
+
+    stored_model = line_value("Model")
+    current_model = str(getattr(agent, "model", "") or "").strip()
+    if stored_model and current_model and stored_model != current_model:
+        return False
+
+    stored_provider = line_value("Provider")
+    current_provider = str(getattr(agent, "provider", "") or "").strip()
+    if stored_provider and current_provider and stored_provider != current_provider:
+        return False
+
+    return True
+
+
 def _get_continuation_prompt(is_partial_stub: bool, dropped_tools: Optional[List[str]] = None) -> str:
     if is_partial_stub and dropped_tools:
         tool_list = ", ".join(dropped_tools[:3])