What is the posibility for Str::random to create same string upon each app isntance in multi-server webapp?

I am making this model in my laravel Application.

namespace AppModels;

use IlluminateDatabaseEloquentFactoriesHasFactory;
use IlluminateDatabaseEloquentModel;
use IlluminateSupportStr;

class ApiKeys extends Model
{
    use HasFactory;

    const TABLE = 'api_keys';
    protected $table = self::TABLE;

    public static function boot()
    {
        parent::boot();

        self::creating(function ($model) {
            $model->identifier = Str::random(16);
        });
    }
}

And upon Identifier I want to ensure that contains a unique random string:

use IlluminateDatabaseMigrationsMigration;
use IlluminateDatabaseSchemaBlueprint;
use IlluminateSupportFacadesSchema;

return new class extends Migration
{
    public function up(): void
    {
        Schema::create('api_keys', function (Blueprint $table) {
            $table->id();
            $table->string('name');
            $table->string('identifier')->unique('unique_identifier');
            $table->boolean('active');
            $table->timestamps();

        });
    }

    public function down(): void
    {
        Schema::dropIfExists('api_keys');
    }
};

But my application runs in multiple instances behind load balancer:

Would this cause not unique random strings be generated, in other words could Str::random(16) (and the underlying function openssl_random_bytes) generate non unique string if both executed from multiple instances?

In order to avoid this usually I prepend the hostname:

  $model->identifier = gethostname()."_".Str::random(16);

But this makes the identifier look ugly or even expose some infrastructure information. How I could avoid this?