Just a reminder that this is the equivalent of spray painting a poster put up somewhere by the FSB, and doesn’t constitute any kind of incursion into any system the FSB relies on or cares about.
The FSB going out of their way to proactively ensure the site maintains 100% uptime even in the face of a rare, massive, and temporary DDOS campaign is expensive and a waste of resources. If you're going to focus your resources on keeping a website that hardly even matters up 100% of the time, you're going to end up having your IT organization disrupted in a far more meaningful way. The organization as a whole has limited resources and is regularly dealing with defending against the most advanced APT's in the world from infiltrating its network and disrupting its activities. Good stewardship of IT means good prioritization.
Saying that the FBI infiltrated Anonymous is like saying that they’ve infiltrated antifa; it’s a category error.
For most of its existence, 420chan has been plagued with administration incompetence and downtime, so I find it very hard to believe someone who can't even run a site is secretly masterful at hacking them.
That is almost the definition of the "hacker group Anonymous". It / They are a swarm of swarms of undefined individuals who join these various swarms based on their own ideologies, motivations, availability, skills, and current level of life boredom.
This is it's greatest strength: if it hits "viral internet meme" popularity, it can actually achieve a productive level of coordination / chaos with no specific 'head' that can be cut off.
It's also it's greatest weakness: As you've described, the ability to (mis)attribute blame, ie. "state cyberattack disguised as ..." because there is no cohesive group to need the reputation points of claiming responsibility.