Does the noble verse: (فَتَشْقَى - so you would suffer) mean that suffering is destined for males only, excluding females, and that a righteous man holds a higher status than a righteous woman, or receives a greater reward?

The word "tashqa" (you toil) in the verse includes both Adam and Eve, for toil and hardship in this world are not exclusive to males over females. The reward and recompense for worship increase with the increase of hardship and expenditure, for the reward is commensurate with the difficulty.