Is paying a sum of money to a person who intervenes to finalize a stalled legal visa transaction—without this person having a direct relation to the transaction—considered a form of bribery or not?

If the person will follow up on the transaction and obtain the visa lawfully, in a way that does not violate Islamic law or secular law, then there is no harm in paying him money as a fee for completing the transaction. This is not considered a bribe, but rather a permissible ju'alah (commission/reward for a task) in Islamic law, as evidenced by the Almighty’s saying: "And for he who brings it is the load of a camel, and I am responsible for it."