Issues after update to TYPO3 10

I have upgraded a TYPO3 installation from 9.5.26 to 10.4.15 and encountered two problems.
First this PHP error:

PHP Fatal error: Declaration of TYPO3\CMS\Core\Crypto\PasswordHashing\SaltedPasswordService::init() must be compatible with TYPO3\CMS\Core\Authentication\AbstractAuthenticationService::init(): bool in /typo3/sysext/core/Classes/Crypto/PasswordHashing/SaltedPasswordService.php on line 82

I suspect the file SaltedPasswordService.php is from an older TYPO3 version, because the extension was merged to core. I have deleted the file and the error no longer occurs. Can this still cause problems and should I also delete SaltedPasswordsUtility.php?

And regarding the second error - when logging into the backend I get this error:

[CRITICAL] request=“d6f236152d270” component=“TYPO3.CMS.Core.Error.ProductionExceptionHandler”: Core: Exception handler (WEB): Uncaught TYPO3 Exception: Argument 1 passed to TYPO3\CMS\Belog\Controller\SystemInformationController::appendMessage() must be an instance of TYPO3\CMS\Backend\Backend\Event\SystemInformationToolbarCollectorEvent, instance of TYPO3\CMS\Backend\Backend\ToolbarItems\SystemInformationToolbarItem given | TypeError thrown in file /typo3/sysext/belog/Classes/Controller/SystemInformationController.php in line 50. Requested URL: /typo3/index.php?route=%2Fmain&token=–AnonymizedToken-- - {“TYPO3_MODE”:“BE”,“exception”:{}}

If I disable the extension belog I can use the backend normally. I can also re-enable belog when I am already logged in without any problems. What is the problem here? I would like to have belog permanently active.