I want to know when we last ran the package upgrades/updates on our Debian server.
/var/log/apt/history.log gives you information on when APT was run and what was done.
tail -3 /var/log/apt/history.log
will give you this information for the last run of APT (not necessarily the last run of upgrage, though).
To find out when was the last time you've run an upgrade, you want to look for a line starting with
Upgrade: and then lookup up the timestamp in the following line of the file (which starts with
End-Date:). The last such match is the last time you've run an upgrade.
Outside of lucking out on log files located in
/var/log/apt - e.g.:
The closest thing I can think about is to examine dpkg:
ls -alt /var/lib/dpkg/info | head -n 10
The dates on the top should approximate the last time apt handled those packages.