fix(ui): thread header counts only queued items; label the live dot

ui/src/lib/components/app-sidebar.svelte

@@ -84,11 +84,13 @@
       open ? "p-3" : "items-center p-2"
     )}
   >
+    <span title="event stream from the gateway (SSE)">
       <LiveDot
         detail={gateway.live.detail}
         label={open}
         state={gateway.live.state}
       />
+    </span>
     {#if open}
       <div class="flex items-center justify-between gap-2">
         <span class="truncate text-muted-foreground text-xs">

ui/src/lib/panel/conversation-header.svelte

@@ -45,6 +45,9 @@
 
   const WINDOW_MAX = 56;
   const windows = $derived(info.bindings.filter((b) => b.visible));
+  const queued = $derived(
+    info.queue.filter((item) => item.status === "queued").length
+  );
 
   const SEEDS = [
     { label: "clean - empty context", value: "clean" },
@@ -196,9 +199,12 @@
     <span class="tabular">
       last activity {fmtRelative(info.last_activity_at)}
     </span>
-    {#if info.queue.length > 0}
+    {#if queued > 0}
-      <span class="tabular font-medium text-note">
+      <span
-        {info.queue.length}
+        class="tabular font-medium text-note"
+        title="messages waiting for the next turn"
+      >
+        {queued}
         queued
       </span>
     {/if}