floppinux VS meta-raspberrypi

tinycore has WAY more functionality than OP is looking for. floppinux crams a stripped out but modern kernel and busybox onto a single floppy. tbh it's still a lot of bloat for what OP wants.

You can still do this. Here's kernel v5.13 and Busybox booting from floppy on a 486 laptop with 24M RAM: https://github.com/w84death/floppinux

I was playing with floppinux about a year ago (and fixing it to actually work on 486 and 586 class hardware, because that's the sort of thing I spend time on). It's modern Linux parts (5.x kernels, modern musl, etc.) that still fits on a floppy.

Have a go for yourself: https://github.com/w84death/floppinux

How do you figure Pis have bad integration with Yocto?

https://github.com/agherzan/meta-raspberrypi

For what it's worth, the entire Pi lineup is also well supported by Buildroot. In-tree, no less.

Embedded linux exactly. Major OEMs are using yocto. Check https://www.yoctoproject.org/

Been there. You don't want alpine or debian. Good gpos, but what you want is Yocto, which will let you build exactly and only what you need piece by piece including only the kernel modules for your hardware, the exact applications you use and no extras, and with a little extra tweaking, you can wire in Mender for ota updates and the ability to push custom images to clients that need specialization, or even fully unlocked images for customers that need it, plus if you're using an SD card, you can send users recovery drives instead of shipping full devices or let them build their own images without your proprietary code

I second Yocto. It's the kernel in use by the OpenBMC project

One last "option" is yocto but tis is not good for desktop, but it can be a fun project.