Alright, going back to the OP, I'll throw in my $0.02:
How far back do you think the modern world could "operate" normally on?
This is actually really tough to answer. I'd say that the biggest sticking point would actually be the economy as a whole, however high-frequency trading goes back to the '90s when it was legalized. I think that it would be safe to assert that the minimum system requirements for the modern world are some sort of 486en. The 486 was a massive leap forward in terms of performance due to its pipeline and integrated FPU (in the DX models). All that has been done since then is the addition of more pipelines and the hardware to make efficient use of them. The 486 was also the sort of unofficial requirement for proper preemptively multitasked modern OSes (the 386 was technically the base minimum, but only by a veeery slim margin).
If process tech were still allowed to advance, we'd first see accelerator cards for video decompression, etc become popular, followed by a massive push for clock rates, followed by parallelism. We'd end up in the same place, but with hardware that would seem very foreign to us now.
If process tech were not allowed to advance, then I'd expect dual-socket motherboards to become popular in the desktop computer market as performance gains could not be made by cranking clocks or tech. After the dual-socket revolution, I'd expect there to be to be integration of multiple dies on the same substrate a la the Pentium D.
If everyone's iphones, androids, and i7's disappeared for example.
If it all disappeared, I'd expect people to first be extremely angry, but they'd get used to it (if you took my desktop away, I'd scream at you for about a week and then stare at you sullenly for a while before buying a shiny new 486.) The PC market would completely tank, however, as an unfortunate number of the people introduced to computers by the internet and mobile revolutions would be unable to handle Windows 95 and DOS-esque operating systems. After the resulting crunch and perhaps economic collapse, I'd expect programmer wages and job security to rise massively as it would become a more specialized skillset with greater resistance to outsourcing.
Another interesting effect is that HD television would disappear overnight, as the hardware resources to encode and decode it would far exceed available computational capacity. Whatever few factories still manufacture CRTs would likely enjoy their sudden windfall as people replaced their now magically broken flat panel TVs with tech that was viable in the 486 era.
Would the 15 year old kid with his i5 still be a "gamer" if all he had was a 386?
Yes, yes he would. In fact, I think that the gamer/PC enthusiast segment would be thrilled to know that it is now the entire PC market, and that hardware manufacturers would cater only to their wants and needs.
Would the libraries be filled with people sitting on computers if all the computers were DOS machines?
Ehhh, it depends. Libraries would still likely have computers available for people to use (especially if they could set up some sort of book search system on them), but I wouldn't expect them to be full of people using those computers.
To be honest, I have an optimistic outlook of the whole thing, because people like us who actually use and cherish this sort of hardware would suddenly be in demand 🤣
Dual Katmai Pentium III (450 and 600MHz), 512ish MB RAM, 40 GB HDD, ATI Rage 128 | K6-2 400MHz / Pentium MMX 166, 80MB RAM, ~2GB Quantum Bigfoot, Awful integrated S3 graphics.