I dont't own a framework laptop, but for the brightness control you might need to enable some other _LEDS options to your kernel.
There are quite many of those:
I would assume the default distribution kernel will have the support.
Fastest and easiest way would be to quickly install
gentoo-kernel-bin or
vanilla-kernel-bin and see if if the issues disappear. If so, you should be able to fix the problem by adjusting kernel configs.
You stated, that
dmesg shows the keyboard disconnecting (normally) and reconnecting right after. You didn't see any errors? Only disconnect+connect messages?
Also make sure your kernel has loaded the module(s) from
app-laptop/framework-laptop-kmod (use
lsmod to see).