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.