Found a good working browser for Win2k! · 4:58pm Mar 20th, 2019
https://retrosystemsrevival.blogspot.com/2018/05/palemoon-265-for-windows-2000.html
I'm at school right now, but testing it in Windows 10 shows that it supports HTML5 standards quite well!
According to the site linked above, Palemoon 2.65 (A fork of Firefox) was backported by an independent developer to Windows 2000!
Let's just hope that that also includes i586 compatibility.