Welcome!
You're right, this feature doesn't exist on Linux. You're not the only one to have noticed:
https://obsproject.com/forum/threads/deactivate-device-when-not-in-use.187700/
To explain a little why there's no progress... A lot is change going on with Linux outside of OBS. The big one is the migration away from
X11 (which displays windows) towards
Wayland. Along with this,
PipeWire is becoming a big player in how audio and video data is passed from one application to another - this includes webcams.
The end result - is that a lot of the
OBS development is geared towards having these up and running; and its not going into adding features to the "old"
V4L2 libraries for using webcams.
I actually did make some progress on an underlying issue that would prevent the stopping + starting of an asynchronous source; but it hasn't been merged:
https://github.com/obsproject/obs-studio/pull/12431
If you stick with Linux, you'll get used to being in the minority of the users for lots of software: that can have its downsides. On the upside though, my system (running Ubuntu MATE) is so much snappier, more stable, and less glitchy than Windows 11 - and I would never
ever go back.