As far as using core rope with relays, you'd probably need to wrap each wire around the core many times (transformer-style) to get enough voltage to trip a relay. The raw signals from cores are really small and hard to detect even with ICs.
Relatedly, Jacquard Looms were some of the earliest punch card-based "computers" as well.
There's probably some set of interesting bootstrap paths to general computing entirely from the textile world.
Although I do like the sound of your idea...
I suppose computers really are fancy clockwork. So are humans.
We don't really understand how the brain works, but it does seem that neuronal integration is an analog and probabilistic process, quite different from deterministic responses in computers (or clockwork). Some people have even speculated about quantum mechanical effects, though those hypotheses are very controversial and I don't put much stock in them personally.
It's overly reductive to compare the brain to a computer, and the analogy tends to obscure more than it illuminates.
https://mindmatters.ai/2018/08/the-brain-is-not-a-meat-compu...
https://aeon.co/essays/your-brain-does-not-process-informati...
We as humans might be missing the right equations/right measurements/precision to actually figure out it's exact state.
We are just accustomed to computers being electrical. In the end it's all binary and we just happen to all use digital input and output.