Download update before asking for restart Every now and then my Mac informs that there is an Update that needs a restart to install. Once I click on Details, there is a Button to install the update and restart. But once I click that one, there is a Download of more than a gig pending.

I would like to change this behaviour, such that the notification only appears when the Update is already downloaded. Is that possible? How can I achieve this?

Checking "Automatically keep my Mac up to date" doesn't seem to have any effect.
You might need to check the boxes "Check for updates" and "Automatically download updates when available" for the download. Also, Check firewall options for allowing connections if denied.

https://forums.macrumors.com/threads/where-are-downloaded-software-updates-stored.1629444/ and as I too verified, updates are located in Library/Updates before install.  You can verify if it is available for install or not.