Is it permissible for me to take an overtime allowance from the municipality, knowing that I do not perform any additional work, and that my basic salary is paid by another entity, and this allowance was disbursed as a substitute for a secondment bonus that was not ministerially approved?

If the official has the authority to process the mission allowance in this manner until approval is received, then there is no harm in taking the bonus, even if it is called an overtime allowance. However, if this is not within his authority, then it is not permissible to take it, because the director does not have the right to dispose of the entity's funds except with permission, and unlawfully dipping into public funds is forbidden by Islamic law.