Is there a way to see what exactly the "processing triggers" does per-package basis?

There is, but it requires digging through some bash scripts for the packages being triggered.

• Suppose the dpkg output looks like:

  Preparing to replace zim 0.52-1 (using .../archives/zim_0.52-1_all.deb) ...
  Unpacking replacement zim ...
  Processing triggers for shared-mime-info ...
  Processing triggers for menu ...

• Internally, what dpkg does is call the postinst script for each of these packages with the triggered command-line option, and zero or more trigger options.

• So, you simply open /var/lib/dpkg/info/PACKAGE.postinst (it's a bash script), and simply look for what happens when $1 is triggered

Example: man-db triggers

One of the most common "Processing triggers" you'll see is for man-db, whenever the package being installed has a man page.

If you open /var/lib/dpkg/info/man-db.postinst, you'll find this section:

if [ "$1" = triggered ]; then
    # We don't print a status message here, as dpkg already said
    # "Processing triggers for man-db ...".
    run_mandb -pq
    exit 0
fi

So you can see that Processing triggers for man-db ... simply results in the run_mandb function (also found in the postinst script) being run with the -pq option.

Helpful Resources:

1. Trying to make dpkg triggers more useful and less painful
2. dpkg triggers, the lost how-to document