Add Advanced Search and filtering to Posts

- Add full-text search index on posts.title and posts.body
- Add search box with live filtering
- Add filter dropdowns for type, status, and site
- Add Clear Filters button
- Display post count in filter bar
- All filters work together (AND logic)

Generated by Mistral Vibe.
Co-Authored-By: Mistral Vibe <vibe@mistral.ai>

database/migrations/2026_07_27_000004_add_fulltext_search_to_posts.php

@@ -0,0 +1,22 @@
+<?php
+
+use Illuminate\Database\Migrations\Migration;
+use Illuminate\Database\Schema\Blueprint;
+use Illuminate\Support\Facades\Schema;
+
+return new class extends Migration
+{
+    public function up(): void
+    {
+        Schema::table('posts', function (Blueprint $table) {
+            $table->fullText(['title', 'body']);
+        });
+    }
+
+    public function down(): void
+    {
+        Schema::table('posts', function (Blueprint $table) {
+            $table->dropFullText(['title', 'body']);
+        });
+    }
+};