fix: resolve streaming messages splitting into individual bubbles

Simplify addMessage/updateMessage to only write to messages.value,
add syncMessagesToSession() to copy messages back on session switch
and stream completion. Also fix mobile viewport, session list overlay,
hamburger logo, and various responsive improvements.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

src/components/layout/AppSidebar.vue

@@ -315,7 +315,7 @@ function handleNav(key: string) {
 
 .sidebar {
   width: $sidebar-width;
-  height: 100vh;
+  height: calc(100 * var(--vh));
   background-color: $bg-sidebar;
   border-right: 1px solid $border-color;
   display: flex;
@@ -448,6 +448,12 @@ function handleNav(key: string) {
     display: none;
   }
 
+  .status-row {
+    flex-direction: column;
+    align-items: flex-start;
+    gap: 8px;
+  }
+
   .sidebar {
     position: fixed;
     left: 0;
@@ -459,6 +465,11 @@ function handleNav(key: string) {
     &.open {
       transform: translateX(0);
     }
+
+    // Override global utility — sidebar is always 240px wide
+    .input-sm {
+      width: 90px;
+    }
   }
 }
 </style>