Refactor BarButton to use rounded shape and update AI Chat tab hint to utilize BarButton

Tinycast/DesignSystem/BarButton.swift

@@ -1,16 +1,16 @@
 import SwiftUI
 
-/// A bar control's hover chrome. The footer's buttons are capsules; one that opens a menu takes
-/// that menu's own corner instead, so the control and what it opens read as one piece.
+/// A bar control's hover chrome. The footer's buttons are capsules; a header control takes the
+/// menu row's own corner instead, so every control along that row reads as one family.
 enum BarButtonChrome {
     case capsule
-    case menu
+    case rounded
 
     var shape: AnyShape {
         switch self {
         case .capsule:
             return AnyShape(Capsule())
-        case .menu:
+        case .rounded:
             return AnyShape(
                 RoundedRectangle(cornerRadius: Theme.Radius.menuRow, style: .continuous))
         }
@@ -66,7 +66,7 @@ struct HeaderMenuButton: View {
     }
 
     var body: some View {
-        BarButton(chrome: .menu, action: action) {
+        BarButton(chrome: .rounded, action: action) {
             HStack(spacing: Theme.Spacing.sm) {
                 switch icon {
                 case .symbol(let name):

Tinycast/Palette/RootPaletteView.swift

@@ -543,15 +543,17 @@ struct RootPaletteView: View {
     }
 
     /// Nothing else advertises Tab, so the launcher says where it goes — the footer's own pairing
-    /// of a label with its cap, never a click target: the header belongs to the field.
+    /// of a label with its cap, and the click does exactly what the key it names does.
     private var aiChatTabHint: some View {
-        HStack(spacing: Theme.Spacing.sm) {
-            Text("AI Chat")
-                .font(Theme.Typography.bar)
-                .foregroundStyle(Theme.Colors.textSecondary)
-            KeyCapChip(text: "⇥", style: .outline)
+        BarButton(chrome: .rounded, action: cycleMode) {
+            HStack(spacing: Theme.Spacing.sm) {
+                Text("AI Chat")
+                    .font(Theme.Typography.bar)
+                    .foregroundStyle(Theme.Colors.textSecondary)
+                KeyCapChip(text: "⇥", style: .outline)
+            }
         }
-        .allowsHitTesting(false)
+        .help("Open AI Chat  ⇥")
     }
 
     /// Resolved through `PaletteTabAction` rather than restated, so the hint cannot promise a