My Mac mini M4 won't update to macOS 27.2

First check if your Mac is compatible with macOS 27 Golden Gate. That will depend on the specific model. Apple’s current compatibility list is here:

macOS 27 Golden Gate is compatible with these computers - Apple Support

If you are not offered an update in System Settings and/or are unable to install an update downloaded via Terminal, then is likely that you are in Low data mode. Users have reported difficulty upgrading macOS over Wi-Fi in Low data mode, and that toggling that setting OFF enables them to perform a Software Update. 

Turn off Low data mode

• Open System Settings 
• Click on Wi-Fi
• Click on the Details button on the right side of your connected network
• Toggle the setting off

More info from Apple: Wi-Fi settings on Mac - Apple Support

If macOS 27.2 does not appear in Software Update, try the following steps in order.

1. If you are using a VPN, shut it off.

2. Restart your Mac.

3. Go to System Settings > General > Software Update and check again. Press Command-R to refresh that settings pane, just in case.

If macOS 27 still does not appear, you can check which software updates are currently being offered to your Mac.

Open Terminal (find the app with Spotlight or in Applications > Utilities) and paste the following, then press return:

softwareupdate --list-full-installers

If macOS 27.2 appears in that list, you can download the full installer with:

softwareupdate --fetch-full-installer --full-installer-version 27.2

It has been reported that if the update attempts to install but fails before completing, and your Mac stays on the previous version of macOS, that if you are in Lockdown Mode than disabling that will allow the update to install normally.

Many thanks neuroanatomist,

Turning off low data mode worked. The OS upgraded from 27.0 without problem. When it happens on my iPad I get an alert about low data mode but not on MacOS, it just says MacOS is up to date when it ain't.

If you have enabled lockdown mode, that's why

Need to disable lockdown mode before upgrading

Otherwise, provide more details as to what happened