Depends on the anarchist. Many would focus on seeking the absence of involuntary power hierarchies. A manager who distributes work and does performance evaluations isn’t intrinsically a problem, it’s when people doing the work can’t say “no, they’re a terrible manager and they’re gone”, or you can’t walk away from the job without risking your well-being.
Anarchists and communists/socialists have a lot of overlap. There’s also overlap with libertarians, except libertarians often focus on coercion from the government and don’t give much regard to economic coercion. An anarchist will often not see much difference between “do this or I hit you” and “do this or starve”: they both are coercive power hierarchies.
Some anarchists are more focused on removing sources of coercion. Others are more focused on creating relief from it. The “tear it down” crowd are more visible, but you see anarchists in the mutual aid and community organization crowds as well.
Anarchism is opposition to power hierarchies, specifically non-consensual or coercive ones. Wealth inequality without safety networks is a coercive power hierarchy, and so needs to be fought. Capitalism as a whole is almost always incompatible with anarchy, at least in the way we tend to do it now. In a system with strong social safety networks the choice to work for someone can actually be a choice, and so some schools of thought would view it as compatible.
Others view exclusive ownership of property as someone asserting power over someone else’s ability to use said property, and therefore wrong. Needless to say, abolition of private property is not compatible with capitalism.