Is saying "for the sake of Allah" – after having an inner monologue about the anticipated increase in wages as compensation for current vows – considered a new vow for that increase?

A vow is not binding unless it is made with a صيغة (formulation) that indicates commitment and intent, both of which are absent here. The mentioned formulation did not indicate commitment, nor was it made with intent; rather, it was a slip of the tongue. Therefore, you do not have a new vow upon you.