feat(web): mobile bottom action bar for + New server

On phones the dashboard top bar is tight with the nav icons + the primary
action crammed alongside. Move the action into a sticky bottom bar in the
thumb zone, leave the top bar to navigation. Hidden on the create-wizard
route since that page owns its own action.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

apps/web/app/(dashboard)/layout.tsx

@@ -1,4 +1,5 @@
 import { Logo } from '@/components/logo';
+import { MobileActionBar } from '@/components/mobile-action-bar';
 import { FileClock, LayoutGrid, Package, Server, Settings } from 'lucide-react';
 import Link from 'next/link';
 
@@ -29,13 +30,14 @@ export default function DashboardLayout({ children }: { children: React.ReactNod
           </div>
           <Link
             href="/servers/new"
-            className="inline-flex h-7 items-center gap-1.5 rounded-md bg-[--color-accent] px-2.5 text-[12px] font-medium text-white transition-colors duration-200 hover:bg-[#5557e8]"
+            className="hidden h-7 items-center gap-1.5 rounded-md bg-[--color-accent] px-2.5 text-[12px] font-medium text-white transition-colors duration-200 hover:bg-[#5557e8] sm:inline-flex"
           >
             + New server
           </Link>
         </div>
       </header>
-      <main className="flex-1 bg-[--color-bg]">{children}</main>
+      <main className="flex-1 bg-[--color-bg] pb-20 sm:pb-0">{children}</main>
+      <MobileActionBar />
     </div>
   );
 }

apps/web/components/mobile-action-bar.tsx

@@ -0,0 +1,35 @@
+'use client';
+
+import Link from 'next/link';
+import { usePathname } from 'next/navigation';
+
+// Routes where the global "+ New server" CTA makes no sense — the wizard is
+// itself the create flow and owns its own primary action.
+const HIDDEN_PATHS: readonly string[] = ['/servers/new'];
+
+/**
+ * Mobile-only sticky bottom action bar. On phones the dashboard top header is
+ * already tight with the nav icons; the primary action belongs in the thumb
+ * zone, not crammed top-right. Hidden from `sm:` upward where the header has
+ * room for the same button inline.
+ */
+export function MobileActionBar() {
+  const pathname = usePathname();
+  if (HIDDEN_PATHS.includes(pathname)) return null;
+
+  return (
+    <div
+      className="fixed inset-x-0 bottom-0 z-40 border-t border-[--color-border] bg-[--color-bg-elevated]/95 backdrop-blur sm:hidden"
+      style={{ paddingBottom: 'max(env(safe-area-inset-bottom), 0.5rem)' }}
+    >
+      <div className="mx-auto flex max-w-7xl px-4 pt-2.5">
+        <Link
+          href="/servers/new"
+          className="inline-flex h-11 w-full items-center justify-center gap-1.5 rounded-md bg-[--color-accent] text-[14px] font-medium text-white transition-colors duration-200 active:bg-[#5557e8]"
+        >
+          + New server
+        </Link>
+      </div>
+    </div>
+  );
+}