The Remote Control feature needs to be enabled in Zoom via the web portal to be able to share control of your screen.
In your Zoom meeting settings, turn on this setting:
Remote control - During screen sharing, the person who is sharing can allow others to control the shared content.
To record a Zoom Session: https://support.zoom.com/hc/en/article?id=zm_kb&sysparm_article=KB0062627