Webex on macOS Sonoma: share your screen and allow remote control

How can somebody see my screen?

Start sharing in Webex and stop again straight away. That sounds roundabout, but it is the trick: macOS only lists an application after it has asked once. Before that you will look for it in vain.
Open the Apple menu at the top left and choose System Settings . Faster: press Command+Space and type " System Settings ".
Go to Screen & System Audio Recording .
Lets the application read what is on the screen — which is what the others then see.
System Settings > Privacy & Security > Screen & System Audio Recording
Open Settings nowOpens System Settings directly at the right place. If nothing happens, the path beside it gets you there just as well.
Find Webex in the list. If it is not there at all, the + below the list is the way in.
Turn on the switch next to Webex .
tccutil reset ScreenCapture Cisco-Systems.Spark
In the meeting click Share and choose the whole screen.
Now really quit Webex — Command+Q, not just closing the window — and start it again. macOS does not apply a freshly granted permission to a running application, and this is exactly where most people get stuck: everything is set correctly and it still does not work.

Everything in the section above still applies. Only this is added:

Go to Accessibility .
Lets the application move the mouse and type. Without it somebody can watch, but touch nothing.
System Settings > Privacy & Security > Accessibility
Open Settings nowOpens System Settings directly at the right place. If nothing happens, the path beside it gets you there just as well.
Find Webex in the list. If it is not there at all, the + below the list is the way in.
Turn on the switch next to Webex .
tccutil reset Accessibility Cisco-Systems.Spark
Go to Automation .
Lets the application control other applications. Some meeting applications ask for this in passing.
System Settings > Privacy & Security > Automation
Open Settings nowOpens System Settings directly at the right place. If nothing happens, the path beside it gets you there just as well.
Find Webex in the list. If it is not there at all, the + below the list is the way in.
Turn on the switch next to Webex .
tccutil reset AppleEvents Cisco-Systems.Spark

How to tell which permission is missing — the symptoms resemble each other, the causes do not.

Screen recording: The share starts but the others see only an empty or black picture.
Accessibility: Control has been granted but nothing responds.
Automation: Some applications cannot be controlled remotely while others can. Only when: When Webex asks whether it may control another application. Once dismissed, macOS does not ask again by itself.