Avot refers to Avot Beit Din! and that's because it is connected to Masechet Sanhedrin - hence its location in N'ziqqin.
[FWIW Bartenura kinda alludes to this defintion!]
Defintion of Pirkei [or Pirqei]?
Pirka is a Shabbat afternoon study group.
I will repost the long version BEH
Avot refers to the middot and wisdom needed to act as an Av Beth Din and became a Shabbat Afternoon TextBook - probably during the Ga'onic era