Huh? The one thing you generally can't update is the kernel since it's the foundation of every other process. I haven't used ubuntu in several years, have things changed drastically?

There were three large patches that were integrated into the Linux kernel in version 4.0 (2014) that make it so that you can live patch the kernel easily. [0][1][2]

(Before these arrived there were already some tool's for it, for some distros. But now everyone should be able to, unless the distro intentionally cripples the ability).

[0] https://lwn.net/Articles/619390/

[1] https://lwn.net/Articles/622936/

[2] https://lwn.net/Articles/634649/

Only if you register for Canonical Livepatch Service. Standard Ubuntu still requires reboot.

They do kexec ? (And no, ksplice/kpatch, if they are using that is not booting a new kernel.) I would be kinda worried about long term system state in that case...

I'm confused by your question. Kexec is a reboot, at least as currently implemented, and that comment does not claim that it's "booting a new kernel".

Only partially: you can apply some bugfix and securit patches, but straight upgrades to a new kernel version still requires a reboot.