It's highly unlikely the internet would still exist in an anarchist type society. One issue, of many, is the internet needs fuel to produce energy (electricity) for it to run and stay online. That would need to be done in areas all over to keep it online. How would anarchists be able to produce enough energy for the gazillion servers? The options are limited to the types of fuel, which are wood, fossil fuels (coal/oil/natural gas), nuclear reactor, and "clean" energy to use to produce the energy needed to keep the internet online. Wood would be a bad option to use for fuel to produce energy. It would practically require an entire forest just to kind of keep the internet running for a little while. That's presuming that all the energy produced from wood was dedicated to keeping the internet online. It definitely would cause a bunch of negative things to the environment, animals, and people living in that area and elsewhere.
The next would be fossil fuels, but that'd required a bunch fairly organized groups/bureaucrats willing to share it, retrieve the coal/oil/natural gas from the ground, process and refine it, determine where to ship it, and the act of shipping it itself. A whole host of issues and problems would come from trying to do something like that; from degradation of the environment, pollution, filth-iffying air and the water supplies, spills...etc. If the area you lived in had coal and everyone in the group was okay with mining it, they could use it to produce energy to keep the internet online and other technology. They could also conceivably refine coal into liquid fuel (gasoline/diesel) for cars or any gas powered machine needed for transporting. The Nazis converted coal into diesel prior and during WWII. However, if doing something like that, I doubt keeping the internet running would be anywhere near a top priority. That's if other anarchists groups even tolerated it. It would definitely piss off anarchists living in surrounding areas because they'd have to deal with the filth and pollution produced by some other group's coal plant, mines, reactors...etc.
Nuclear power would be kind of similar to fossil fuels in that there'd need to be people living in that area that is okay with mining for uranium ore and rare earth metals. Mining for those materials would turn that area into an insta-shithole. Not to mention people and animals would likely end up developing various types of cancer, and a host of other issues involving animals, humans, fishies, and the environment. If an anarchist group did get a nuclear reactor working, there'd need to be a place to dispose of the radioactive nuclear waste. A nuclear reactor also needs an outside source of energy to run it, backup generators, and a consistent source of water to limit the possibilities of a meltdown. It'd also require an tightly organized group/bureaucrats to make sure it goes smoothly, and if they decide to share with others. I imagine no one would be willing to take nuclear waste off of the people running the nuclear reactor, nor would any anarchists within 30 miles be pleased with some other group running a nuclear reactor. An accident or meltdown would irradiate areas within 5 to 30 miles of the reactor.
Finally there's "clean" energy like hydroelectric dams, solar panels, wind turbines, water turbines...etc. Those wouldn't provide enough energy to keep the internet online by themselves. It too would require organized groups/bureaucracies to keep them functioning. Damming up rivers or attempting to would piss off people downstream. It would put people in a situation where the group that built the dam would have control over people downstream. It would further mess up migration of animals and fishies.
So, assuming anarchists could be able to do each of those things and were willing to do so. It would just be a recreation of the machine of today. There'd be a large amount of bureaucrats. Bureaucrats galore!! To make it worse, there would probably be meetings everyday especially if it was an anarcho-communist or syndiaclist land. They really like meetings and direct democracy from what I've gathered. Just imagine going to a meeting after working in the mine all day developing black lung and/or radioactive lung so people elsewhere can use the internet or any energy intensive technology. To me, I would be confused as to what actually changed.
Personally, I think some anarchists would realize quickly what was going on, would not be okay with reproducing the state and current technology, and would try to prevent it. I've seen people on anarchist message boards discuss that they'd keep the current technology fully functional without realistically explaining how they plan to accomplish that. If their explanation sounds like Star Trek magic or other sci-fi magic (like mining asteroids), then it's safe to dismiss them imo. In conclusion and 9 years in the making, when you hear or read anarchists discussing maintaining current technology and/or developing more advanced tech. Then I think it's best to briefly think about how these anarchists would realistically go about producing the energy needed for any energy intensive technology, like the internet. And maybe think about if that's desirable or not to you and/or why.