Visibility phase 5: public /explore directory + search

A no-login directory of shared trees, backed by GET /api/v1/public/trees:
- /explore: searchable grid of public trees; debounced name search. Because the
  backend adds `site_members` trees when a valid session is present, signed-in
  users see more with no client-side branching.
- PublicHeader extracted and shared by /p and /explore (logo, Explore, Sign in).
- "Explore" entry added to the authed sidebar.

tsc clean; next build passes.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
Signed-off-by: Justin Paul <justin@jpaul.me>

frontend/app/explore/layout.tsx

@@ -0,0 +1,10 @@
+import { PublicHeader } from "@/components/public-header";
+
+export default function ExploreLayout({ children }: { children: React.ReactNode }) {
+  return (
+    <div className="min-h-screen">
+      <PublicHeader />
+      <main className="mx-auto max-w-5xl px-4 py-8">{children}</main>
+    </div>
+  );
+}