Identifying this type of pin header soldered to the board
That type of pin was (and perhaps still is) called &quot;SIP pin&quot;. They were available in different lengths, and made to fit different PCB thicknesses.
You will still find some little breakout boards with those fitted (for example, from Capital Advanced Technologies Inc. - I don't have any connection with the company) but as you know, nowadays the square header pins are more common on breakout boards.
Those SIP pins could also be used to convert early SIMM memory modules, into (now obsolete) SIPP memory modules. More about that (and some photos) at: Wikipedia - SIPP memory.
I actually found a datasheet for the SIP pins used by the above company on another website, but couldn't find it on their own website (at least, not any more). So here is the 1 page datasheet:

Image source: Manualzz