I managed to make it work in my Manjaro (Arch-based) Linux with this (thanks to the hint here)
Install the current Linux headers:
sudo pacman -S "linux$(uname -r | awk -F. '{print $1$2}')-headers"
Install (and build) the v4l2loopack-dkms
sudo pacman -S v4l2loopback-dkms
Load the module with the option for fakecam:
sudo modprobe v4l2loopback devices=1 video_nr=20 card_label="fakecam" exclusive_caps=1
(you may need to unload it if you have it already in, with sudo modprobe -r v4l2loopback
)
Now fakecam
(the snap installed with the package manager) works, after enabling it with snap connect fakecam:camera
.

...for quite small values of "working":*
- It's quite slow,
- It fails to detect my body --- the floating head is a bit unnerving
- Teams for Linux is unable to access the stream (black camera), so it's of little utility.
I will try later, or let this open to other people, to see if with https://github.com/floe/backscrub works better.