Is money earned from a non-engineering job, which the questioner does not perform, considered halal or haram, while he continues to work as an engineer for the contractor, on the basis that this money is an appreciation for his efforts that exceed his current salary?

This administrative procedure is permissible. What is given in exchange for work is lawful to benefit from, as long as the entrusted work is performed as required. The difference in the job title from the nature of the work does not affect this, as it is a purely administrative procedure undertaken by the head of the government entity for the benefit of the work, and there is no harm in that.