Believe it or not, the nebulous nature of the department actually is what makes them more likely to have qualified immunity because their role hasn't been "clearly established" by case law. You couldn't even talk say what "actions as a part of their duties" are. I'm not a fan of qualified immunity.
As far as suing the government over what DOGE does, good luck figuring out where an agency deputized by executive order fits in here: https://en.m.wikipedia.org/wiki/Federal_Tort_Claims_Act
Blue ringed octopus is just using tetrodotoxin though, it's not like they developed that toxin through evolution. Bacteria are the ones that made TTX so toxic. I'm not impressed.