Not having lib32 packages in KaOS means virtualbox is packaged very different from the distros you mention.
There is no need to re-install, but on any kernel change, not just updates, also when you decide to boot into any other kernel like linux-next or linux-lts and back to regular linux after that, you need to run:
sudo /usr/bin/vboxsetup setup
If you want to run that line at every start-up (which will delay start-up), you can add a sercive file similar to:
edit line 8 with the above vboxsetup line, rename it to vboxsetup.service and enable it.
I don't think all/most vbox users would want this as default behavior for KaOS.