Since updating your M3 MacBook Air to macOS Tahoe 26.7.1, the built-in camera has stopped working.
You have already restarted and fully shut down the Mac, and Camera access is enabled under System Settings >> Privacy & Security>> Camera.
What is unusual is that the Mac’s built-in camera is not listed there at all, while your iPhone camera is. You are also seeing the green camera indicator flashing.
I would first check System Settings >> Screen Time >> Content & Privacy >> App Restrictions and make sure Camera is allowed.
It is also worth checking App Limits to make sure the app you are testing is not restricted. (support.apple.com)
Next, try the camera in both Photo Booth and FaceTime.
Also go to System Settings >> General >> Software Update and see whether another macOS update is available.
The most useful diagnostic check is to open Apple menu >> System Information >> Hardware >> Camera
See whether the built-in camera is listed.
If it is not , that would indicate that macOS is not detecting the camera, rather than this simply being an application permission problem.
If the built-in camera remains unavailable and the green indicator continues to flash, Apple says that the Mac may need to be serviced. (support.apple.com)
Have the computer evaluated by the Professionals who have the Special Hardware Software and Expertise to diagnose the issue and offer possible solutions
Make an Appointment at the Apple Genius Bar or call 1 800 MyApple and have them evaluate the computer
Other location Call Centres
Contact Apple for support and service