On the question as to if they were battle or parade items ...I think over time they were both but looking at the David Collection at
https://www.davidmus.dk/en/collectio...ar/art/12-1979 and I note;
Quote“Blows were dealt with battle-axes tabar-i-zin, clubs, and swords. A red mist rose from the river.”
(Firdawsi, Shahnama, 10th century)" Unquote.
Certainly the Qajar Dynasty which only ended in about 1923 adds to the concept that axes were for parade work...Earlier, however, (though I still search for more facts ) it appears that Saddle Axes were meant as the antidote to Cavalry in heavy armour which were effective against swords were susceptible to a blow from a Saddle Axe...
What is interesting is what appears to be an early form of battle axe called a Parashu...which I will place in a fresh post.