It does. My understanding is that as long as the police don’t make the suggestion, then it’s not entrapment.
If the officer asks, “hey, do you wanna bomb that building?” it’s entrapment. If you ask “would you help me bomb that building?” and the officer sells you what you think is a bomb, it’s not. Of course, the officer isn’t necessarily wearing a wire or anything, and it’s possible to phrase things carefully to suggest something without literally making the suggestion, so it comes down to the officer’s testimony (“I never suggested that he commit a crime” and maybe “I did suggest that somebody ought to pay for that behavior”) versus the accused’s.
My understanding of entrapment is that it's convincing someone to do something they wouldn't ordinarily. I don't think "Wanna bomb that building?" Qualifies as entrapment. It would be difficult for undercover police to catch drug dealers, for example, if they couldn't ask the dealers to sell them drugs.
Entrapment would be more like "We're going to bomb that building, and if you don't join us, I'm going to kill you... Hah! Just kidding, you're under arrest!"
"Government agents do not entrap defendants simply by offering them an opportunity to commit a crime. Judges expect people to resist any ordinary temptation to violate the law. An entrapment defense arises when government agents resort to repugnant behavior such as the use of threats, harassment, fraud, or even flattery to induce defendants to commit crimes."
With the terrorism examples it seems like a form of peer pressure is the main force used, which may not make it a crime but it still feels like entrapment.
"Sting" operations are nothing new for the FBI. And depending (as your link states) how the FBI goes about it (case in point[0]), it may or may not be "entrapment."
By any reasonable interpretation, it is entrapment, and a fair number of lawyers out there were pretty unhappy, some vocally so, with the outcome of that whole shitshow.
Please compare and contrast "reasonable" and "legal" interpretations.
While such a comparison might rub you (and me, for that matter) the wrong way, it's the "legal" interpretation that holds in a US Article III court[0].