>Direct democracy might work well for a city state where even poor citizens are independent land owners,
One of the principal beliefs of Anarchists is that property is theft[0]. So no one would be an independent land owner. Everyone would be equally involved and have equal rights as we would all be members of the Commune/Council/Community/Collective/Union/whatever term the community wants to use to describe their collective. I prefer either Commune or Union personally.
>But I'm not convinced it would work for a large nation where there are enough powerful bad actors that they can use marketing and patronage to get control of the political process.
A lot of people have this idea that Anarchism would break down at larger levels. And that's kind of true, but we have organizational techniques to avoid this. One such technique is the idea that you have your commune and it's you and your neighbors or coworkers (you can be in multiple communes) and it will be a small commune where everyone knows each other. This is the group that handles most of your day to day governance and issues. These communes will federate with other communes, and create a commune that are represented by a member of each member commune. These representatives would represent the will of their source commune in the larger federation, and can be instantly recallable if they start making power plays or decisions that the source commune doesn't agree with. There could be multiple levels of these federations, each keeping the group in session small (less than 80 people) but no one really being in a position of power or permanently having their job. Each commune that's part of the federation can choose how they choose their representative. Some may want the most charismatic person. Some may choose at random. Some may consider it a duty of the members of that commune and so it switches every few weeks. These representatives don't get special perks or privileges for being chosen. They just represent their federation and their commune in order to expedite the process.
Also, Anarchists do not believe in the concept of the City State, or the Nation. Borders are violent[1].
[0] https://en.wikipedia.org/wiki/Property_is_theft! [1] https://crimethinc.com/posters/borders-the-global-caste-syst...