Jo22: what would you like to run on a 486 with modern Linux? Or are you mainly wanting to keep i486 kernel support for posterity's sake? Assuming i486 was supported, could a DX4-100 w/modern linux be turned into a decent router?
The oldest computer I have in the house which runs Linux for normal tasks is a P4 3.8 GHz Prescott w/hyper threading. It runs Ubuntu 16.04 LTS and still barely receives critical security updates. This is my garage computer and I only use it when doing mechanic work, usually to look up factory service manuals or watch youtube videos on car repair. That system can barely cope with these minimalistic tasks. To speed it up some, I put in a SATA3 card with a modern SSD. Even in this use case, one might consider such a setup self torture. For me, I find it barely good enough for the task. Upgrading to a new distro would make it even slower.
i486 w/Ubuntu 24.04 LTS, assuming there was support, could run what well? Would it not be preferred to use an older Linux distro with a solid modern router, rather than waiting 3 weeks for your i486 to boot-up and start Chromium?
Plan your life wisely, you'll be dead before you know it.