Any Linux desktop OS can be made "lightweight", e.g. just use i3, xfce4 apps and
disable the convenience daemons you can live without.
The real bottleneck is a web browser that can render the modern web and there is no real solution for that.
The real bottleneck is a web browser that can render the modern web and there is no real solution for that.
I think ChromeOS solves that problem quite smartly, by starting the bare necessities to launch the browser and nothing else. No more moving parts, just the web, which is what 99% of computer use seems to be these days anyway.
ChromeOS Flex seems to work pretty well for giving old laptops a second life. It won't run on your Pentium II but there are plenty of computers out there that'll work great.
With Microsoft's plans for Windows 12, I can imagine a cloud-based Windows that you can use any old laptop with. As long as you have decent WiFi and a thin client loaded, you'll end up with laptops where hardware h264 decoding will matter more than CPU power and RAM.