How to "catch" max execution time error in php

use Illuminate\Support\Str;

class Shutter {
  
  public function shutdown()
  {
    if ($this->hasTimeoutOccurred()) {
      dump('timeout');
    }
  }
  
  private function hasTimeoutOccurred(): bool
  {
    $lastError = error_get_last();
    
    if (!$lastError) {
      return false;
    }
    
    if (Str::startsWith($lastError['message'], 'Maximum execution time')){
      return true;
    }
    
    return false;
  }
}

ini_set('max_execution_time', 1);
$shutter = new Shutter();
register_shutdown_function(fn() => $shutter->shutdown());

while(1);

public function shutdown()

if ($this->hasTimeoutOccurred()) {

if (Str::startsWith($lastError['message'], 'Maximum execution time')){
   return true;
}

$shutter = new Shutter();
register_shutdown_function(fn() => $shutter->shutdown());

1. I don't like to pass in the callable as string, it is error prone, the IDE doesn't recognize it as a function, and it is ugly.
2. The arrow function doesn't have it's own scope, so it inherits the parent's scope, therefore I can access the instantiated variable without the use($shutter).