After doing a search, I've found two comment threads on https://community.linuxmint.com/ that deal with this exact same issue:
5 years ago: https://community.linuxmint.com/idea/view/1680
4 years ago: https://community.linuxmint.com/idea/view/3100
And a more recent discussion here:
https://github.com/linuxmint/cinnamon-sc...issues/142
This seems to confirms that Mint update indeed does not notify the user when there is a system reboot needed.
5 years ago: https://community.linuxmint.com/idea/view/1680
4 years ago: https://community.linuxmint.com/idea/view/3100
And a more recent discussion here:
https://github.com/linuxmint/cinnamon-sc...issues/142
This seems to confirms that Mint update indeed does not notify the user when there is a system reboot needed.