I've confirmed that I got the point release update to 20.04.3 LTS with lsb_release -a, but uname -r shows that my kernel is still on 5.4.0-81-generic. Should I not be on 5.11? My machine running Ubuntu 21.04 is on 5.11.0-31-generic.
I found an old thread here which proposes using apt to install linux-generic, but I wanted to make sure it was still good advice.
Presumably you are running Ubuntu 20.04 LTS on this machine because you have determined that it's more important for this machine to be stable rather than having newer, more bleeding edge software.
Ubuntu 20.04 currently uses Linux Kernel 5.4 unless you have enabled HWE or have manually upgraded the kernel beyond the version in repositories.
Unless you actually need the newer kernel version, it might be better to leave it alone if stability is more important to you than the newest versions of software.
You have to enable HWE stack for kernel by
See release cycle for actual kernel versions.