. . .Continued from above

if that society is able to pool that surplus it can create things that the individual members wouldn't be able to create on their own

Yes. And there are more ways than one to pool resources. It can be done communally (e.g. simple agreements to share the resource, usually with democratic mechanisms to administrate access and use. i.e. an individual, at some level, will dictate, but his/her authority is subject to the vote), it can be done via borrowing and lending or investment and contractual agreements on demanded returns, etc. (i.e. an individual dictates, but his/her actions are subject to enforcement of the agreed-upon contract and the outcomes of their actions, as they are financially liable, i.e. skin in the game). It can be done via decentralized autonomous organization (such as crypto contracts, assurance contracts, and the like). It can be done via gift or grant, from some philanthropist who has previously amassed a much larger share of society's resources (hopefully through merit and production of value rather than theft, or fraud).

However, this is still an anarchist society as it is a small number of people all agreeing on how to use their resources. So anarchism is definitely viable on a small scale.

You'll note though here, that logically, there is nothing precluding any of the many possible arrangement which fall into the above scenario from scaling. We'll get into your arguments of course as to why you think it doesn't scale, but it first needs to be acknowledged that nothing precludes it, and that the scenario you described does not even go into enough detail to make a judgement as to whether the economic and political arrangements could scale.

The village has specialized labor and wants to pool its resources to build a library. However, this requires a lot of people to pool their money, and people to agree on certain rules of how to run the library. Most people don't know each other in that village, and they certainly can't all get together and agree on a specific course, there are too many people for that to be practical. So they appoint an organizational body to manage the specifics of this project. We now have government.

All you're describing is a classic public goods problem. And, in fact, the greater complexity, size, and specialization of labor in society are irrelevant and unnecessary in order to make this case and go straight for the libertarian jugular, so to speak. The production of public goods (highly non-rivalrous, and non-excludable) is indeed a "market failure", in that they tend to be under-produced on the market, by way of pareto optimality... when produced privately, or in the method of private goods production. But no, we do not necessarily have a government here (again, government being distinguished from governance or other forms of cooperation by the use of coercion). We have ways in which to produce this public good, publicly, but not using government. Now, there are ways also to produce libraries, or the intended benefits of libraries, privately. . . but we're going to concede that they will be under-produced privately, and that in any case, there is an argument to be made about the aesthetic of the mode of production (i.e. people don't want the library under private, for-profit control, even if this private administration ended up acting the same way as the public administration). So, let's assume that the production of this library is a hard, binary, public good. Modeled after what we, in our society now, think of as the hallmark features of a library. How do we produce this library without it being a loss-leader of some rich private guy, and also without using coercion of government in order to overcome the public goods problem? Obviously, few people will pay into, or pool their resources into the building and maintaining of this library, if they know that others will not be excluded from enjoying it even if they don't pay (i.e. the classic free-rider problem). Here's some mechanisms we can use, which do not employ force, theft, manipulation, taxation, or coercion of any kind:

Assurance contracts- A bunch of us want a library, we feel that most other people do too, so we form our own little association, and this association publicly makes known of the proposed project and allows people to opt in, pay their money into an escrow, which is triggered or legally turned over to the association for execution of the project, if a pre-specified reserve is met. No one loses money if the required reserve is not met. . . no one need hesitate to donate due to fear of the free-rider problem.

Lottery- A bunch of us want a library; we feel most others do too. We form a little association and pool our money for liquidity, and then start selling lottery tickets, or raffles, or run a casino; wherein the proceeds (minus the winnings) go towards funding and maintaining the library. Lotteries overcome public goods problems, because players voluntarily fund more of the project than they would otherwise, at the prospect of winning even more money than they put in. Chance is a powerful motivator of human beings. There is a good reason governments tend to monopolize gambling and lotteries. It would not do for them to let people see how well public goods can be funded without them, and most governments themselves also fund a not-insignificant portion of their expenses through lottery.

Value Add- This isn't likely going to be as applicable to this particular case of building a library, but I'm showing you mechanisms (which can of course be mixed and matched with the private modes and the public mechanisms just listed). Historically, things like lighthouses were produced without government, by making the public good simply a value-add; such as building a harbor and charging entry (i.e. the usefulness of the lighthouse is non-excludable and public, but the harbor is excludable and the proceeds from the harbor fund the lighthouse).

Continued. . .