composer.json

{
    "require": {
        "symfony/error-handler": "^5.3"
    }
}

index.php

<?php

require_once 'vendor/autoload.php';

use Psr\Log\AbstractLogger;
use Symfony\Component\ErrorHandler\ErrorHandler;

ErrorHandler::register()
    ->setDefaultLogger(new class extends AbstractLogger {
        public function log($level, string|\Stringable $message, array $context = []): void
        {
            $formattedLogLine = sprintf(
                '[%s] %s: %s%s'.PHP_EOL,
                date('Y-m-dTH:i:s.uP'),
                $level,
                (string) $message,
                ($context['exception'] ?? false) instanceof \Throwable
                    ? sprintf(' in %s:%s', $context['exception']->getFile(), $context['exception']->getLine())
                    : ''
            );

            file_put_contents(__DIR__.'/deprecations.log', $formattedLogLine, \FILE_APPEND);
        }
    }, \E_DEPRECATED | \E_USER_DEPRECATED)
;

// "null" argument deprecated as of PHP 8.1
var_dump(str_contains('foo', null));