I've thought a lot about this before. Updoot because it's a good question.

Basically, if an anarchist society still has access to all of the books and such for long enough, someone somewhere eventually will figure it out. Blowing them glass bulbs is surprisingly uncomplicated once you have metallurgy (tutorial), you don't even have to use mercury for the vacuum if you happen to have a regular factory built compressor nearby (will one from a fridge work? nobody knows, nobody tried), which you can then rebuild later. Build some circuits using wood + nail and metal wires as the PCBs, do random things to see how it reacts and learn from it. Now, electricity itself and metallurgy are fun but out of scope for this explanation.

While that is happening, people can reuse existing TV boxes, routers and such. Someone could do a tiny C program or something to distribute data over the existing computers or something, then advertise it over (real life) bullet-in boards. Ironically, I suggest more distributed solutions (whenever possible/feasible of course) over something like this site, or usenet (R.I.P., now just full of piracy). Non-technical people can get their friends to help with using that. People who where previously sysadmins for ISPs and stuff should then probably allow just port scanning IPv4 to discover other people, and/or the v6 multicast (well, hopefully they can figure that out if they haven't been "docker-washed" or whatever). Now, once someone figured something out, they share it with the comrades and "advertise" it using that solution. Or again, just the real life bullet-in boards.

If there are enough good minds, they can then proceed to basically skip "regular" transistors and diodes (and maybe even real PCBs, although some already do that at home) and go straight for the micro fab. Now, it requires many fields of science. Like first, you need to take a few buckets of sand, containing rocks and shells and shit (literally), then purify it. Like, really really really fucking pure. This is where my personal level of expertise ends but I am sure that eventually some talented people in their own respective fields can meet up and think of something over an afternoon. From what I know (probably wrong), this basically involves melting it in a vacuum, unmelting, melting, unmelting and so on, then from the piece that formed you have to cut off the edges where all of the impure stuff ended up. Now, you need to make patterns on it. This guy figured it out but gave in and started a company. Basically, instead of the template you shine light through, you could substitute an office projector for something really shitty scale and really shitty reliability, but functional. The rest is mostly chemistry... idk I don't speak chemistry.

Now, you can go get someone who speaks transistor logic to implement some really shitty instruction set in hardware. I am sure it wouldn't be too complicated to address map a teletype for some I/O. First few programs can be in ROM right inside the CPU (with redundant bytes of course given how shitty the manufacturing is) for testing, until RAM is figured out.

Oh look, my new chip draws boobs on paper!

Then you, again, go share your findings with the society and find someone who still has a RISC-V design or something downloaded. Now, that might get good enough to run a multi user operating system (this will make sense soon). As much as we hate the C stdlib and all of it's tech debt, I am not sure if anyone will be up for redoing all of that (yet). I have been shilling OpenBSD a lot lately, but for something like this I would imagine NetBSD would be more fitting. Plan 9's stdlib is MUCH better (and there's a functional WIP RISC-V port), but to properly use that you will need pointing and CRT tech so it's kind of a circular loop there, and it's also not as accessible due to being mostly GUI and due to having lots of single letter commands/shortcuts to remember across the included programs. Although whatever you can get your dirty hands on (I am being slightly pessimistic (or realistic, even) and assuming not having access to the internet at this stage, the one and only as we know for being controlled by the big IANA). Fork the OS you got. Most tools have been generally designed around some level of hierarchy, although for source control, git and compatibles (got...) remain best (thanks, Torvalds 2005). The reason is sharing patches over plain text, and more importantly applying them, becomes trivial (if you add a signature/checksum, even more so, as you now know it wasn't corrupted or line converted or anything). Allow anonymous editing like for TCC to minimize said hierarchy (maybe invent a better solution later, like something distributed with proof of work for voting if a patch gets in or not... too bad all of this terminology has been taken by crypto bros). (EDIT: proof of work kind of sucks since capitalist rich kid can get 70 computers) Speaking of TCC, that's a nice ass compiler, should probably use that to avoid hogging the tiny brain you've just built for others. "What others", well...

Here's the part where a multi-user OS starts making sense. As soon as networking starts to network, put it right onto the usual networks with existing repurposed computers from before. Let it be like a pubnix, or "shell provider" if you like calling it that. Let people fuck around, find out ("help I deleted authorized_keys"), maybe even discover backdoors and other bugs. While that is happening, go improve, go make more, go offer some units IRL to especially interested people. Obviously, share the hardware designs, so someone also especially dared could do the office projector thing, while someone else is trying to figure out how to replace the said office projector with something more DIY.

And basically, there you go. Now, this is technically possible under de-facto capitalism; although I am not sure if anywhere on this planet right now exists a community of especially dared, IRL connected and unoccupied enough in time people.

EDIT: figured someone might want to use this text.

            DO WHAT THE FUCK YOU WANT TO PUBLIC LICENSE
                    Version 2, December 2004

 Copyright (C) 2004 Sam Hocevar <sam@hocevar.net>

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            DO WHAT THE FUCK YOU WANT TO PUBLIC LICENSE
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  0. You just DO WHAT THE FUCK YOU WANT TO.