Was the reason for the revelation of the hijab to differentiate between the free woman and the slave woman, and what is the wisdom behind this differentiation? And why did Umar used to hit slave women if they wore the hijab, and how does that align with preventing fitna?

It is incorrect to say that the reason for the obligation of the hijab is to differentiate between free women and slave women. The correct view is that the Sharia differentiated between them regarding the issue of hijab or the limits of awrah (nudity), and this is the madhhab (school of thought) of the majority of scholars. The majority supported this differentiation with the story of the Prophet's marriage to Safiyyah (may Allah be pleased with her). However, there is a difference of opinion on this matter, as some scholars equate free women and slave women in terms of awrah, citing the generality of Islamic texts and that temptation (fitna) does not differentiate between them. Al-Albani responded to the hadith of Safiyyah by stating that it negates the niqab (face veil), not the jilbab (outer garment), meaning that a slave woman may not have her face fully covered, but she must cover the rest of her body. Sheikh Al-Islam Ibn Taymiyyah affirms that if there is fear of temptation from a slave woman, she must observe hijab, and men must lower their gaze from her. He also states that the differentiation between free women and slave women in hijab is not absolute but is linked to time and the presence of temptation.