For positive experience while taking an exam on Mac (macOS), proper computer settings configuration is a must.
macOS Mojave 10.14+
On your Mac, choose Apple menu > System Preferences, click Security & Privacy, then click Privacy.
Click Camera.
Select the checkbox next to an app to allow it to access your camera. Deselect the checkbox to turn off access for that app.
If you turn off access for an app, you’re prompted to turn it on again the next time that app tries to use your camera.
macOS Catalina 10.15+ or Big Sur
Turn on screen sharing on your Mac:
On your Mac, choose Apple menu > System Preferences, then click Sharing.
If Remote Management is selected, deselect it.
Select the Screen Sharing checkbox. Choose Google Chrome in the apps list.
Turn off App Limits for your web-cam:
Choose Apple menu > System Preferences > Screen Time > Content & Privacy > Apps.
Make sure that your camera is flagged.
Choose "App restrictions". To use your web-cam with an app from the list, make sure that the "Limits" flag is not set.
Save settings and relaunch Google Chrome.
If you see that the settings cannot be updated, you may need to unlock changes. Click on the lock icon to do so. You will need to enter your admin name and password to unlock changes.