Watchdog Script
Since this should be a one-liner, I'm going to do it in a markdown file to explain my thought-process.
The command that will produce the output we want is du -hd0 /var /home. This will likely need to be run as root, since root is generally the only user that can see the entirety of /var.
To run it repeatedly without using watch, we can put it in a while true loop, like so:
while true; do du -hd0 /var /home; sleep 60; done
I figure 60 seconds is a decent middle-ground here, but honestly this is a fairly expensive command to have running all the time, since it needs to recursively read the metdata of every file in the directory to calculate the directory's size. If this kind of monitoring needs to be run frequently, it would be better to set up the system such that /var and /home are on their own filesystems (a BTRFS subvolume or ZFS dataset would work as well), and then use either df -h /var /home (if on their own volumes) or the appropriate filesystem-specific command in order to report the space used by these directories.
If this is running in a daily cron job or some such, with the reports being emailed to the system administrator, then performance shouldn't be an issue, and we can simply run the du command.