With macOS Catalina (10.15), Apple introduced new security and privacy features for your Mac.
In order to capture and share screen recordings with Jiminny, you have to grant your browser access to the Screen Recording permission. By default, this permission will stop you sharing your screen.
To start, enter the conference room and click to share your screen. You should get a prompt asking you to grant access.
Click "Open System Preferences" and allow your browser (e.g. Google Chrome, Firefox) to access the Screen Recording permission.
You might need to authenticate first by clicking the lock icon in the bottom left corner of the window.
Afterwards, you will have to restart your browser. Now you are ready to go!