There's not any reason to do anything special beyond a usual sudo apt update and sudo apt upgrade on your OctoPi image. The OctoPi image is still based on Buster, rather than Bullseye - you won't get the updates that are in that article on the OctoPi instance. They don't look particularly relevant, as many are only for GUI use which OctoPi does not have.
If you want to use Bullseye (and so you can have the updates mentioned), you will have to use an OctoPi 1.0.0 release candidate, or nightly build.
I tend to fall in the "if it ain't broke, don't fix it" camp when it comes to updating. As long as it's working fine and there's no new features I absolutely need or critical security issues to address, I just leave it be