New MacBook Air - update installation failed
I had to disable System Integrity Protection (SIP). Just follow this answer:

https://apple.stackexchange.com/a/361046/333653

Then I had to open a terminal and delete all folders in /Library/Updates with sudo rm -Rf e.g. sudo rm -Rf 041-57076. These are the update files, I need to delete them because they are corrupted because of poor internet connection.

Now I triggered the update again, it began to download the update again and now it works :)

If it does still fail, then try this procedure again, but connect via cable not via Wifi.