No, 'operating system' lives in rootfs too, together with things installed later by you. 'operating system' is just major subset of packages already preinstalled.

But incidentally it looks like old rootfs works with newer kernel and initfs from 2.2006.39 so it theory it is possible to reflash just the kernel and initfs from newer firmware and keep old rootfs. But this may be even more unstable than both old and new systems. But maybe not :-)

That way you may get some improvements caused by newer bluetooth and wi-fi firmware (which lives in initfs) and still keep older main system in rootfs if you feel it is more stable.

But of course this is completely unsupported :-)