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/components/app-sidebar.tsx

@@ -4,6 +4,7 @@ import {
   Archive,
   ArrowDownUp,
   BookText,
+  Compass,
   FolderTree,
   Image as ImageIcon,
   LogOut,
@@ -92,6 +93,7 @@ export function AppSidebar({ onNavigate }: { onNavigate?: () => void }) {
       </Link>
 
       <Item href="/trees" label="Trees" icon={FolderTree} active={pathname === "/trees"} />
+      <Item href="/explore" label="Explore" icon={Compass} active={pathname === "/explore"} />
       <Item href="/import" label="Import" icon={ArrowDownUp} active={pathname === "/import"} />
 
       {treeId && (

frontend/components/public-header.tsx

@@ -0,0 +1,23 @@
+import Link from "next/link";
+
+// Slim header for the public (no-auth) surface: /p/* and /explore.
+export function PublicHeader() {
+  return (
+    <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>
+        <nav className="flex items-center gap-4 text-sm">
+          <Link href="/explore" className="text-[var(--muted)] hover:text-[var(--foreground)]">
+            Explore
+          </Link>
+          <Link href="/login" className="text-bronze hover:underline">
+            Sign in
+          </Link>
+        </nav>
+      </div>
+    </header>
+  );
+}