How the whole "Copyrighted Music" is affecting you
You have probably had an awesome livestream only to see that the sound has been removed from major parts of the VOD afterward and therefore have no material to download and re-publish on fx Youtube. This is primarily because of copyrighted music playing in the background.
The harsh truth is that if you are not licensed or approved to use copyrighted music then you are breaking the copyright law, even if you are licensed to listen to the music privately through fx Spotify or Tidal. Obtaining a license for private use does, unfortunately, not include a commercial distribution license - which is what you need when streaming the music to other people, even if it is free of charge.
License through Network Partners
Even if you obtain the legal rights to distribute their music on your channel your face being muted because Twitch needs to know you have the appropriate rights. If your network is not automatically informed twitch about this, that is. You should also be aware of where you are licensed to distribute this music. If the license does only accept the music to be used on YouTube then it would still be illegal to use on Twitch and vise versa.
You can always use non-Copyrighted material
If you do not want to go through all the work and assurance, just to know if you are allowed to use a specific song or piece of music in your videos or on stream, you can always be on the lookout for non-Copyrighted music. What that means is that the original author or owner hereof have publicly licensed the material to be used however you like - as long as you do not commercialize (sell or claim) the material as if it was your own.
Just make sure to double-check if the content is actually 'non-Copyrighted' and not just labeled as it is. If you want to find such music, there is plenty of networks collecting this music and publishing it for you to download off of them. Non Copyrighted Sounds is an example of such a channel. If you want to know for sure, then check out their guidelines.
If you are not sure if you should still obtain a license from them, go through this formula and they will help you figure it out.