Discord added a feature without putting it in the patch notes -- the ability to have screen sharing in server voice channels. According to Discord, and I quote, "This is an experimental feature pushed out to random users and servers...." Thankfully, there's a way around the randomness. This bot allows you to convert your voice channel into a video channel (temporarily).
This bot generates a link to force your Discord client into setting the current voice channel to the active area of the client (ordinarily, only text channels can be set to the active area of the client). From there, you can enable screensharing. And yes, this works on every single voice channel I have tested so far.
However, all users must click this link in order to view the shared video stream.
vc help - Help command.
vc enable - Enable screensharing for current voice channel.
vc permalink - Create a reaction-based button to enable screensharing for current voice channel.
vc about - General information about the bot.
Required permissions: read messages, read message history, send messages, add reactions
Written with discord.py rewrite.