What is the ruling on Umrah, and what is required of someone who walked backward four steps during Say between Safa and Marwah?

Your backward movement during the Sa'y does not harm, because the purpose is to cover the distance between Safa and Marwa, and that has been achieved. In whatever manner the performer of Sa'y walks, it is sufficient for him.

The jurists have stipulated the validity of the Sa'y even if it is performed by walking backward or upside down, as mentioned in Nihayat al-Muhtaj and Fatawa al-Ramli.

And if the intention was to take a few steps backward during the Sa'y, that also does not harm, because it is a slight interruption, and the more apparent view is that continuous succession (muwalat) in Sa'y is not a condition.

Therefore, there is no blame upon you for what you did, and your 'Umrah is valid.