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/p/layout.tsx

@@ -1,20 +1,10 @@
-import Link from "next/link";
+import { PublicHeader } from "@/components/public-header";
 
 // Public viewing surface — no auth, no app sidebar. A slim header only.
 export default function PublicLayout({ children }: { children: React.ReactNode }) {
   return (
     <div className="min-h-screen">
-      <header className="border-b border-[var(--border)]">
-        <div className="mx-auto flex max-w-5xl items-center justify-between px-4 py-3">
-          <Link href="/" aria-label="Provenance — home" className="flex items-center">
-            {/* eslint-disable-next-line @next/next/no-img-element */}
-            <img src="/provenance-logo-plain.svg" alt="Provenance" className="h-6 w-auto" />
-          </Link>
-          <Link href="/login" className="text-sm text-bronze hover:underline">
-            Sign in
-          </Link>
-        </div>
-      </header>
+      <PublicHeader />
       <main className="mx-auto max-w-5xl px-4 py-8">{children}</main>
     </div>
   );