There is a lot of confusion around anarchism, because it is a negative description: It's a collective without leader, without governing institutions. It doesn't say much about how this collective organizes instead. So you could call the chaotic state after a government coup Anarchy. But that isn't what anarchists are talking about and I don't think that is what OP meant either.
Anarchy as a deliberate system is when a group of people decides to work or live together without selecting a leader or any other form of government, instead resolving decisions that affect everyone together. In that sense it is not an interim state, a leadership-vacuum just waiting to be filled. Although of course Anarchy can transition into another system by various means, but so can every other system as well.
There are already a lot of good suggestions here!
I would add Eat the rich and The menu (not related) for movies criticizing the rich. Although the former just makes fun of them.
I would also argue for Andor even though it doesn't focus on the super rich and instead on the rebellion and the people making up the cogs of the fascist imperium. It still shows the rich in a critical light. I haven't seen any series that made me want to fight the system more than Andor.