What is the ruling on one who made a covenant with Allah regarding specific matters, but then was unable to fulfill them due to sleeping through prayers or engaging in backbiting, despite having prior knowledge of his inability to keep his promises?

"A covenant with Allah" is a form of vow (nadhr). If it is intended to compel oneself to do something or refrain from it, it becomes an oath (yameen). If the one who swore the oath breaks it, an expiation for breaking an oath becomes obligatory upon him.

However, if the covenant is to perform an obligation or avoid something forbidden, then you are required to do it by the original Sharia ruling, and its emphasis is increased by the covenant. Expiation does not absolve you of responsibility.

A person must strive in Allah's command, magnify His disobedience (i.e., consider sin grievous), hasten to His obedience, and blame himself, compelling it to obey.