There is no such thing as a pure anarchist. It'd be hard to even define what that is.

You've got the super queer anarcho-nihilists, the hippie anarchists, the avant-garde autonomists who call themselves communists but lean more heavily towards anarchism than Marxism, the standard An-Coms that would claim the legacy of anarchism since the 19th century, the anarchist punks, and even some primitivists. And that's just in America. All of these rather resemble spheres instead of formal ideological camps. There will certainly be a variety of stances from sphere to sphere on unified political programs, whether you should vote at all, the validity of Marxist class analysis, whether any kind of large structured formal organization is worth participating in, the acceptable levels of authority, proclivity for insurrection, whether to use direct democracy or consensus or pure self-direction or something else, and more.

Some movements have general assemblies and movement congresses in which they make decisions thoroughly but excruciatingly slowly. The Zapatistas are used to this and call it "the pace of good governance".

Defining the state is something you can split a lot of hairs over, but I think it can broadly be seen as a formal supra-human entity that exclusively dominates a territory and exercises rights of control not afforded to individuals or smaller groups. If it peacefully overlaps with another entity, or if it doesn't exercise any will that is not a direct wish of the people, or if it has no formal subordination of people and groups to itself but they participate voluntarily, you may call that governance without Government.

Many anarchists have no problem with things being managed by officials at a local level, with safeguards against people monopolizing the seats of power. From there you would have some sort of loose federation of localities, regulating trade and standards and any collective defensive force.

Solidarity without states or hierarchies is pretty easy, you just keep everything horizontal, and you have each person in charge of a part instead of 1 person everyone answers directly to. Sometimes you have someone who's an avowed anarchist yet still ends up sort of being in charge of all the things, drifting into a de facto leader. It sucks when this happens, because it can be a cycle of people deferring to that one person rather than trusting their own agency or pursuing their own development, and also because if anything changes for that person it ripples through all the groups they're a part of.

If there's anything from anarchism you can inform your own politics by, let it be this. Leadership is an umbrella concept, it is a synthetic idea that most cultures did not have until the advent of capitalism, or contact with a bourgeois polity. It is a replacement for the idea of nobility that describes an essence that gives someone the right to rule. In fact, the bourgeois class had to invent the idea of leaders and leadership, in order to displace the ideology supporting feudalism. It is not the sine qua non of effective coordination. In many indigenous cultures, captains of war and spiritual masters have separate roles from the management of the rest of society. The latter is typically done by a group or council of elders, much like how the "alpha wolf" is a total myth, as the senior wolves in a pack are deferred to for their familial relations to other wolves. You don't need to give up the idea of a vanguard party that executes class struggle to embrace leaderlessness. In fact, I think it would make your vanguard party stronger. With separate and rigorous domains of influence, you allow more people to participate and pursue distinction, minimize conflict over who wants to be in charge, prevent most stratification from emerging groups of people who have certain levels of power and people who don't, and reduce any potential impact of infiltration, blackmail, or assassination.