What is the ruling on working in the same commercial field after leaving a job whose owner stipulated not to work in it, and this was agreed upon with the phrase "Allah is a witness between me and you" without swearing an oath?

What you have done is considered a promise, and fulfilling it is among the noble virtues. Allah has described His prophets with it, while breaking it is a characteristic of hypocrites. Scholars have differed regarding the obligation or commendability of fulfilling a promise. The majority consider it commendable, while some have held it to be obligatory. Accordingly, you should not break this promise except for a legitimate Shar'i excuse.