What is the legal legitimacy of this money received by the engineer in exchange for renting his car or as a reward for his diligence in his work, which the responsible manager provides from sums paid by contracting companies without an explicit stipulation in the contract clauses?

The fundamental principle is that a manager is an agent constrained by the authorization of the entity for which he works. If he is authorized to make verbal financial agreements, then there is no blame on him. Otherwise, it is an incorrect action that leads to corruption, bribery, or taking money without the owner's willing consent.

It is impermissible to take anything from this forbidden money if the manager is not authorized to disburse it. Employees must refrain from taking it to put an end to this practice.

It is permissible to claim travel expenses from lawful money if the contract stipulates it. However, it is not permissible to take any of these excesses as bonuses, because they are "disguised bribes."