Is it Islamically preferable to extend the engagement period to increase the suitor's income, or for the fiancée to share in the expenses after marriage, and does this sharing affect the man's Qawamah (guardianship/maintainership)?

A woman spending her money for expenses will be rewarded by Allah, especially if she willingly helps her husband with household costs. This leads to the husband's satisfaction and the family's happiness. This does not contradict the husband's guardianship but rather strengthens it. As for expediting or delaying the engagement, it depends on the wishes of both parties. Hastening marriage is better for safeguarding one's chastity and lowering one's gaze. Allah Almighty has promised the married financial well-being, and Allah's help encompasses the one who marries seeking chastity.