Erm, well my machine is up-to-date, so I’m guessing there may not be any updates to be had at the moment. Generally speaking you can get updates through your “software center” or “software catalog” desktop application.
On the command line, typically on debian based systems there are three different sources for applications;
apt package repository for native applications
snap repository typically for Ubuntu containerised applications
flatpak repository which is a real open source competitor for Ubuntu snap
apt update && apt upgrade # or apt
snap refresh # for snap
flatpak update # for flatpak
There are essentially two types of webcam software;
Local applications (like cheese)
Applications that run inside your browser
The latter rely on your browser to talk to your camera, so as long as your browser is able to talk to your camera, any software (as listed above) that relies on this, should also work. (i.e. everything except local applications that may not be maintained as well as a browser)
In summary, most stuff should work, but it looks like Cheese et al are currently “buggy”.
So yes, just bugs in Cheese and some others … you have to bear in mind that this is all free software, not “all” of it is commercial quality or maintained to commercial standards. (although browsers tend to be …)