IBM PC DOS 2000 was a thing that was published and sold. It would have ran fine on a system similar to what you describe. It addressed the only pressing thing in that space at that time that PC DOS 7 did not: Y2K compliance.

(I never had a PS/2, or ADSL, but I was goofing around with a low-memory 8088 box back then for fun. It had no hard drive. It bootstrapped from floppy, loaded the rest over the LAN with its built-in 10base2 Ethernet jack from my Linux box, and connected to dual-channel ISDN for Internet access. It worked. It even had a graphical web browser.

Being clever with an old iPhone is a very different thing.)