next.js example (#694)

* next.js guide

* better

* shadcn

* fixes

* fix: correct screenshot test assertion to check path instead of base64

The daemon returns { path: savePath } for screenshot commands, not base64.

* fix: cross-platform Chrome detection and gitignore hardening

- Replace hardcoded macOS Chrome path with findLocalChrome() that
  searches common paths on macOS, Linux, and WSL, with a clear error
  message when no Chrome is found.
- Add .env and .env*.local to .gitignore to prevent accidental
  secret commits.

* fix: correct Vercel deploy button repo URL to vercel-labs/agent-browser

* clean up

* demo

* next page

---------

Co-authored-by: ctate <366502+ctate@users.noreply.github.com>

examples/demo/components/ui/separator.tsx

@@ -0,0 +1,25 @@
+"use client"
+
+import { Separator as SeparatorPrimitive } from "@base-ui/react/separator"
+
+import { cn } from "@/lib/utils"
+
+function Separator({
+  className,
+  orientation = "horizontal",
+  ...props
+}: SeparatorPrimitive.Props) {
+  return (
+    <SeparatorPrimitive
+      data-slot="separator"
+      orientation={orientation}
+      className={cn(
+        "shrink-0 bg-border data-horizontal:h-px data-horizontal:w-full data-vertical:w-px data-vertical:self-stretch",
+        className
+      )}
+      {...props}
+    />
+  )
+}
+
+export { Separator }