Conference calls:
You can share your screen on a conference call on your desktop (macOS and Windows) or on Wire for web (Chrome 87 or higher).
1:1 calls
You can share your screen in a 1:1 call on your desktop (macOS and Windows) or on Wire for web (Chrome 87 or higher and Firefox).
Once you're on a call, select the screen sharing button 
.
On macOS Catalina
In addition you need to give access to Wire in your macOS Security and Privacy settings:
1. Access your macOS settings.
2. Select System Preferences, select Security & Privacy, then select Privacy.
3. Select Screen Recording and give Wire access.