I have set up a Discord server with several voice channels. I see no button for the video chat in the lower left corner, so it seems not to be possible to do video chat nor screen sharing. Voice is enabled: I see the microphone, headphone and settings icon.
I have gone into the Server Setting and the Roles there. For the “everyone” role I see connect, speak and video enabled. Also for another role that I have set up, these configuration setting are enabled.
I have other servers with Voice channels where I do see the “Video” and “Screen” button, it is apparently only for this particular channel.
Note a old Reddit post with a similar question: https://www.reddit.com/r/discordapp/comments/aklct9/no_video_chat_button_showing_up_cant_join_video/