Harassment bribe sounds more like if an official were running some sort of unofficial protection racket. But feels like it'd be absurd to punish the bribe giver for that already, considering that the protection racket itself would be illegal.

This paper [1] seems to use the term to describe bribes given to obtain things you're already legally entitled to, which makes a bit more sense. There's an old Indian meme about pensioners having to pay a bribe to get their monthly payment for instance.

[1] https://ideas.repec.org/p/pra/mprapa/50335.html

Because they would otherwise be denied a service or freedom they are legally entitled to. "Undue advantage" is a bribe like "hey choose my company for this lucrative government contract." A harassment bribe is more like "hey here's some money for you to not charge me with a made-up traffic violation", or "hey here's some money in addition to the actual driver's license fee, so that you'll actually do your job and give me my license".