It doesn't seem likely that a parthenogenetic species could develop the sociality to achieve the necessarily cooperative technological advances you say they have. All parthenogenetic species on Earth are loners. Asexual speciation divergence is likely for the time spans you suggest so rather than "Parthans" you'd have a cluster of very similar species.
To answer Why Invent Males? there are two likely intertwined reasons.
a) They decide that divergence is becoming a problem and attempt hybridogenesis (good article on sciencedirect here) which can come in many flavors but also many dead ends genetically (sterile offspring) and
b) They discover that they had arisen that way originally and was the basis for their cooperative society and maybe they were losing that throu a very long time of parthenogenetic reproduction.

Eusociality is what EO Wilson describes as the primary strength of humans: cooperation. There's plenty of debate on how to define it lots of other terms come into play and loads of yakety-yak debate. But without some basic organizational mechanism down at the genetic level there is no way we could have built cities and technology much less a need for language or any conceptual communication (beyond grunting at each other).

Story-wise, even if (as several commenters suggest) there was a role hierarchy going on based on lineage, from one line a "queen" is born. A freak occurrence that allows all their potential genes to be unlocked but they need a separate mate to accomplish this. Or another "queen" is born in another parthenogenetic line, maybe a third, fourth; then a true threat of the Parthans becoming separate species capable of creating their own castes would threaten their collective future presaging a time of competition and warfare. The queens are discovered to have the ability to produce a male, allowing genetic mixing between the current lines and thus avoid all that trouble.

It doesn't seem likely that a parthenogenetic species could develop the sociality to achieve the necessarily cooperative technological advances you say they have. All parthenogenetic species on Earth are loners. Asexual speciation divergence is likely for the time spans you suggest so rather than "Parthans" you'd have a cluster of very similar species.

To answer Why Invent Males? there are two likely intertwined reasons.

1. They decide that divergence is becoming a problem and attempt hybridogenesis (good article on sciencedirect here) which can come in many flavors but also many dead ends genetically (sterile offspring) and
2. They discover that they had arisen that way originally and was the basis for their cooperative society and maybe they were losing that through a very long time of parthenogenetic reproduction.

Eusociality is what EO Wilson describes as the primary strength of humans: cooperation. There's plenty of debate on how to define it lots of other terms come into play and loads of yakety-yak debate. But without some basic organizational mechanism down at the genetic level there is no way we could have built cities and technology much less a need for language or any conceptual communication (beyond grunting at each other).

Story-wise, even if (as several commenters suggest) there was a role hierarchy going on based on lineage, from one line a "queen" is born. A freak occurrence that allows all their potential genes to be unlocked but they need a separate mate to accomplish this. Or another "queen" is born in another parthenogenetic line, maybe a third, fourth; then a true threat of the Parthans becoming separate species capable of creating their own castes would threaten their collective future presaging a time of competition and warfare. The queens are discovered to have the ability to produce a male, allowing genetic mixing between the current lines and thus avoid all that trouble.