Very well, and striped down kernels run on hardware with even less resources today (embedded systems) than 3.1 minimum requirements. If a platform has lost support, and there's sufficient money in it to justify it, you can always go back in time to an older kernel. What really sucks is when a platform vendor maintains their own tree and it gets lost to time.

The real pain is populating the userspace if you need more than just busybox.

There's distros for this: https://github.com/marmolak/gray486linux – it's based on Linux 6.7.

Never used it; don't know how well it works in practice. But it's the type of thing that can be made to work. Looks like some minimum requirements are a tad higher than the minimum of Windows 3.1 though, so it depends a bit on what you mean exactly with "Windows 3.1 era hardware".

As someone who ran Linux on Windows 3.1 era hardware, perfectly well.

Pretty good I would imagine. The first public release of Linux predates Windows 3.1.