And you're missing a key feedback loop. The feds typically "create" an informant by digging up dirt on someone and blackmailing them into ratting on their buddies in exchange for non-prosecution. This informant then has a huge f-ing reason to radicalize the group and see to it that they do or attempt to do something worthy of prosecution so that they can make good on their promise to the feds.
So otherwise potentially benign groups wind up getting turned into hotbeds of extremism basically because the feds demand extremists to prosecute.
This is a workflow that dates back at least as far as the war on drugs where you'd have small time traffickers would get turned into informants and then work tirelessly to push their boss's or suppliers business to the next level while collecting evidince for their handlers. It was used on racist and religious extremist groups in the 80s and 90s and then on muslim religious groups in the 00s and now you're seeing it again with right wing groups.