This bug has been fixed by a recent update in Cheese in both Ubuntu 20.04 and Ubuntu 20.10. The rest of this answer describes the procedure to fix this before the patch was integrated in Ubuntu, I kept it for historical purpose.
The other answer by Paolo provides an workaround using
dconf-editor. This answer provides a method to make Cheese work in the usual way.
End results: CSD Headerbar in Cinnamon (also tested in XFCE and KDE)
This problem only occurs on non-GNOME DEs, even in GTK based DEs like Cinnamon or XFCE.
This has been reported upstream in Cheese application menu / preferences not available on KDE 5 and CSD missing on alternate DEs. A patch has been proposed, but it has not been merged yet.
A user made a PPA with this patch, and reported it to this Launchpad bug report, but it only hosts packages for Ubuntu 20.04.
Solution: For Ubuntu 20.04
Run the following commands to add this PPA to the system.
sudo add-apt-repository ppa:dtl131/mediahacks2
sudo apt-get update
Now, update Cheese to use the patched version.
sudo apt install --reinstall cheese
If you want, you can remove the PPA afterwards.
sudo add-apt-repository --remove ppa:dtl131/mediahacks2
I can confirm that this solution works in
KDE, in Ubuntu 20.04.
If you don't want to add the PPA to your system, and manually download and install the .deb packages with
sudo apt install -f afterwards to satisfy dependencies.
For Ubuntu 18.04, you can use this PPA instead.