Initial GameLog setup

- Laravel 11 + Breeze (dark mode) + Tailwind + Alpine.js
- Migrations: games, genres, platforms, companies, pivots,
  user_games, user_lists, reviews, follows, activities
- Models: Game, Genre, Platform, Company, UserGame, UserList,
  Review, ReviewVote, Activity, User (with gamelog fields)
- IgdbService: OAuth2 token management, search, game fetch,
  popular/new releases, genre filter, cover/screenshot URL helpers
- IGDB credentials in config/services.php (from .env)

app/Models/Game.php

@@ -0,0 +1,76 @@
+<?php
+
+namespace App\Models;
+
+use Illuminate\Database\Eloquent\Model;
+use Illuminate\Database\Eloquent\Relations\BelongsToMany;
+use Illuminate\Database\Eloquent\Relations\HasMany;
+use Spatie\Sluggable\HasSlug;
+use Spatie\Sluggable\SlugOptions;
+
+class Game extends Model
+{
+    use HasSlug;
+
+    protected $fillable = [
+        'igdb_id', 'slug', 'title', 'summary', 'cover_url', 'cover_thumb_url',
+        'release_date', 'release_year', 'rating_avg', 'rating_count', 'review_count',
+        'library_count', 'status',
+    ];
+
+    protected $casts = [
+        'release_date' => 'date',
+        'rating_avg'   => 'decimal:2',
+    ];
+
+    public function getSlugOptions(): SlugOptions
+    {
+        return SlugOptions::create()->generateSlugsFrom('title')->saveSlugsTo('slug');
+    }
+
+    public function getRouteKeyName(): string { return 'slug'; }
+
+    public function genres(): BelongsToMany
+    {
+        return $this->belongsToMany(Genre::class, 'game_genre');
+    }
+
+    public function platforms(): BelongsToMany
+    {
+        return $this->belongsToMany(Platform::class, 'game_platform');
+    }
+
+    public function companies(): BelongsToMany
+    {
+        return $this->belongsToMany(Company::class, 'game_company')->withPivot('role');
+    }
+
+    public function screenshots(): HasMany
+    {
+        return $this->hasMany(GameScreenshot::class)->orderBy('order');
+    }
+
+    public function userGames(): HasMany
+    {
+        return $this->hasMany(UserGame::class);
+    }
+
+    public function reviews(): HasMany
+    {
+        return $this->hasMany(Review::class)->latest();
+    }
+
+    public function scopePublished($query)
+    {
+        return $query->where('status', 'published');
+    }
+
+    public function recalculateRating(): void
+    {
+        $stats = $this->userGames()->whereNotNull('rating')->selectRaw('AVG(rating) as avg, COUNT(*) as cnt')->first();
+        $this->update([
+            'rating_avg'   => $stats->avg ? round($stats->avg, 2) : null,
+            'rating_count' => $stats->cnt ?? 0,
+        ]);
+    }
+}