What is the ruling on working for someone other than the sponsor, and is the money earned from this work permissible (halal) or forbidden (haram), especially since the additional work does not conflict with the primary work? Is the permission of the direct manager sufficient, or must the sponsor's permission be obtained?

As long as the additional work is outside official working hours, does not affect or conflict with the official work, and is not prohibited by the contract, and the prohibition is due to the general law of the state, then the issue falls under the ruler's restriction of what is permissible (mubah (definition)). Violating this restriction is a sin, but what is earned from it does not become unlawful (haram (definition)) if its source was a permissible act. Seeking permission from the manager is not valid unless he is authorized to grant such permission, because the prohibition is for the public interest, not for his personal right.