Is the amount paid to an employer's representative considered a bonus or a bribe, or does it involve a Sharia violation for the institution, whether the work is assigned directly or through a tender where the amount paid does not affect the acceptance of bids?

What the company's representative asks from your establishment is considered a prohibited bribe, because he is asking for money in exchange for his obligatory work for which he already receives a salary from his company, and it is not permissible to fulfill his request. The sin increases if the transaction is a tender and paying the money leads to taking what is not deserved. The way out is to refrain from paying, unless the owner of the establishment is compelled to do so for fear of losing his right.