What does "counter" refer to in "countersink"?

My grandfather was a blacksmith (now long dead). My understanding is that a countersink (also called a bob-punch), is used to form a depression in the surface of plates to be joined together when rivetting. Without this, the head of the rivet projects entirely and is subject to damage. If the head is broken off, the rivet will sink into the plate. The indentation counters any tendency to sink. I suspect the term also applies to indentations for horseshoe nails.

Unfortunately my grandfather and my father are deceased and I can't find anything online to support what I'm saying.

I'll leave this here for now and see if I can find anything further.

Google's Ngram viewer returns results for 'countersink' that indicate that it was a new word in the early 19thC. It does not appear in the corpus at all before 1820 and did not take off until about 1860. This indicates that "countersinking" was a process associated with industrialisation.

The Lexico entry for counter gives an uncommon definition which seems to be relevant.

The back part of a shoe or boot, enclosing the heel.

For which it gives the origin as

Mid 19th century abbreviation of counterfort ‘buttress’, from French contrefort.

The mid 19thC origin of the shoemaking term matches quite well with the appearance of "countersink" in the literature and "countersinking" a hole so that the head of a screw or other fastener fits below the surface certainly improves the strength of the join and could be said to "buttress" the fastener. I suspect that "countersink" also derives, perhaps in part, from counterfort.