Is what is said secretly, without uttering it verbally, in the form of "I covenant Allah" followed by specifying the action, considered a vow?

Mere intention, or thinking about a vow, or resolving to make one, or self-talk, without uttering it verbally, does not necessitate anything. This is based on the Prophet's (peace be upon him) saying: "Indeed, Allah has forgiven my Ummah for whatever crosses their minds, as long as they do not speak of it or act upon it." As for the statement, "I covenant with Allah to do such-and-such," there is a difference of opinion among scholars. Some consider it an oath that necessitates expiation if broken (this is the view of the Hanafis and those who agree with them). The well-known opinion of the Malikis is that it is not an oath. Therefore, if you uttered this statement concerning something permissible, an act of obedience, or an act of drawing closer to Allah, and you did not do it, then according to the Maliki school, you are not required to pay an expiation for breaking an oath. However, it is more cautious to offer expiation if you break it.