The Linux Router Project (https://en.wikipedia.org/wiki/Linux_Router_Project) did that kind of thing in the late 90's and early 2000's. It's long-since dead, however. I doubt there's much of anything today, given the size of the kernel alone.

I built a Linux floppy-based bootable disk imaging environment to roll out masses of Windows 95/98 machines back in 1997-1999. You'd compile a minimal kernel down to 600 - 800 KB then pack-up your userland in an itty-bitty gzipped filesystem archive and concatenate it with the kernel at an even sector boundary, dd the whole thing to a disk, and set some bits to tell the kernel where to load the initrd. I've never gone back to see how much of that functionality still exits in modern kernels. (Very little, I'd assume...)

I used to run Coyote Linux[1] (then BrazilFW) from a floppy on a 133MHz Pentium with a couple of MBs of RAM.

[1]: https://en.wikipedia.org/wiki/Coyote_Linux

I ran one of these for quite awhile, it was fantastic

I used to have one 1.44MB with MS-DOS 3.3 trimmed to the minimum and Turbo Pascal.