Is it permissible for an engineer to include inflated quantities for work not performed by the contractor in the payment certificate in exchange for money, knowing that the state is accused of inciting discord and smuggling funds?

It is not permissible to take a commission from the contractor, as this involves deception, betrayal, and the unlawful consumption of wealth, even if the quantities confirmed are correct. This is only permissible with the permission and knowledge of the ministry you work for. What you mentioned about corruption in the work does not justify you committing what is forbidden, for every soul is held accountable for what it earns. Allah Almighty has commanded the fulfillment of trusts and condemned the betrayal of covenants.