The issue isn't whether it's supported, the problem is that live patching is limited in what it can patch (when functions are inlined it can become impossible to patch them and so on). So while a machine with 4 years uptime might be live patched there are some security issues that cannot be patched that way (for instance, the retpoline patches for Meltdown/Spectre require all function pointers to have different calling conventions and that requires a reboot).
Ubuntu supports it officially, so does Fedora. From my experience it works more or less fine on CentOS, so probably RHEL too. For Suse there is kGraft, so basically >90% of install base supports live patching.
I don't think it's part of the usual Ubuntu distro. I understood you need to register to get it. And it's free (as in beer) only for limited use cases. Don't remember the details.
SLES, RHEL, and Ubuntu all support live patching
https://www.suse.com/documentation/sles-15/book_sle_admin/da...
https://access.redhat.com/documentation/en-us/red_hat_enterp...
I run it on all dedicated servers, as well as managed servers where we can easily pass the cost on.
They're currently releasing livepatches across all the kernel builds to address the Intel MDS stuff (at least the kernel-based mitigations) and it's all very pleasant and hands-off.
Beyond the kernel, you have various libs and binaries that will be replaced during upgrades. All can usually/mostly be restarted without a reboot, but just upgrading packages alone won't guarantee all running processes have been updated.