Carry the rehydrated preview as an option through Sync

sync_effect turned a missing preview into an empty string, which
LivePreview::sync then read as the instruction to clear the host. The
effect carries String? and the DOM side branches on None.

Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Dp6jf4fKxaVzVq2heQR6dX

Author: tonyfettes

desktop/frontend/transcript/component/live_reasoning.mbt

@@ -88,7 +88,9 @@ priv enum LiveReasoningMsg {
 #warnings("-unused_value")
 priv enum LiveReasoningEffect {
   NoChange
-  Sync(target~ : String, step_label~ : String?, content~ : String)
+  // `content` is the stored preview to rehydrate; `None` means the target
+  // has no open preview and the host is cleared.
+  Sync(target~ : String, step_label~ : String?, content~ : String?)
   Append(target~ : String, content~ : String)
   Hide(target~ : String)
   Reset
@@ -133,10 +135,7 @@ fn LiveReasoningState::sync_effect(
       Sync(
         target=target.key.wire(),
         step_label=target.step_label,
-        content=self
-          .preview_for(target.key)
-          .map(preview => preview.content())
-          .unwrap_or(""),
+        content=self.preview_for(target.key).map(preview => preview.content()),
       )
   }
 }

desktop/frontend/transcript/component/live_reasoning_dom.mbt

@@ -218,7 +218,7 @@ fn LivePreview::sync(
   self : LivePreview,
   target : String,
   step_label : String?,
-  content : String,
+  content : String?,
 ) -> Unit {
   if self.target == Some(target) &&
     self.step_label == step_label &&
@@ -231,16 +231,11 @@ fn LivePreview::sync(
   self.cancel_pending()
   self.target = Some(target)
   self.step_label = step_label
-  let host = live_host()
-  if content.is_empty() {
-    self.clear_host(host)
-  } else {
-    match host {
-      Some(host) => {
-        let _ = self.build_card(host, content)
-      }
-      None => self.clear_host(None)
+  match (content, live_host()) {
+    (Some(content), Some(host)) => {
+      let _ = self.build_card(host, content)
     }
+    (_, host) => self.clear_host(host)
   }
 }
 

desktop/frontend/transcript/component/live_reasoning_wbtest.mbt

@@ -47,7 +47,7 @@ test "live reasoning appends by owner and semantic finish deletes it" {
   let (focused, focus_effect) = empty.update(Focused(target))
   assert_eq(
     focus_effect,
-    Sync(target=key.wire(), step_label=Some("#1"), content=""),
+    Sync(target=key.wire(), step_label=Some("#1"), content=None),
   )
   let (first, first_effect) = focused.update(Delta(key, "think"))
   assert_eq(first_effect, Append(target=key.wire(), content="think"))
@@ -57,7 +57,7 @@ test "live reasoning appends by owner and semantic finish deletes it" {
   let (_, hydrate_effect) = live.update(Focused(target))
   assert_eq(
     hydrate_effect,
-    Sync(target=key.wire(), step_label=Some("#1"), content="thinking"),
+    Sync(target=key.wire(), step_label=Some("#1"), content=Some("thinking")),
   )
 
   // The full reasoning event is a semantic boundary, not a durable commit.
@@ -140,7 +140,11 @@ test "live reasoning keeps concurrent conversations and runs isolated" {
   )
   assert_eq(
     focus_effect,
-    Sync(target=local_r8.wire(), step_label=Some("#1"), content="local-current"),
+    Sync(
+      target=local_r8.wire(),
+      step_label=Some("#1"),
+      content=Some("local-current"),
+    ),
   )
   let (with_background, background_effect) = focused.update(
     Delta(remote_r7, "-more"),