Add a search to the showcase

A search app bar looks through every section, example and component,
opens the section, or the example at its anchor on its page, and is
reached from anywhere with / or Ctrl+K. Section pages now carry their
own heading.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01V9NnLxnPp8vaaurb3Z1MFy

docs/plans/livewire-material.md

@@ -594,6 +594,11 @@ pages and the mail theme by an agent in its own worktree. What changed from the
   wire:navigate. It turned up a WebKit bug in `<x-menu>`: inside a focusable region (the shell's
   `<main tabindex="-1">`), WebKit hands focus back to that region as the popover closes, so the
   menu now reads whether focus was inside on `beforetoggle` before returning it to the trigger.
+- **The showcase has a search** in a search app bar (`<x-search>`, `/` or Ctrl+K): an index of every
+  section, every example (by its anchor) and every component, read from the section views and fetched
+  as `/material/search.json` on first focus. Names in a slot's Alpine scope must keep clear of the
+  component's own: `results` and `open` in `<x-search>`'s scope hid the page's. wire:navigate keeps a
+  URL's hash but scrolls to the top, so the layout lands on the hash after the swap settles.
 - **Verified in a fresh Laravel 13.31 application** (`composer create-project`, the package from a
   path repository, the README's CSS, JS and layout, `material:scheme "#4f46e5"`, `npm run build`):
   a Livewire page with an app bar, tabs, a card, a form with validation, a date picker, a dialog and