apt-get count the number of updates available

You could use apt-check from update-notifier-common:

$ /usr/lib/update-notifier/apt-check --human-readable
0 packages can be updated.
0 updates are security updates.

This is the same tool that updates the motd message.

I suppose the fastest method is shown in apticron:

https://salsa.debian.org/debian/apticron/blob/master/apticron#L121-154

This can be distilled to:

apt-get -q -y --ignore-hold --allow-change-held-packages --allow-unauthenticated -s dist-upgrade | /bin/grep  ^Inst | wc -l

You can use apt-get -s to simulate an upgrade process and extract only the number of upgraded packages by

LANG=C apt-get upgrade -s |grep -P '^\d+ upgraded'|cut -d" " -f1

This will result in just the number of packages