If your stream includes popular copywritten music, sections containing the copywritten content will be muted in your VoDs. In my experiences, incidental uses of copywritten music won't get you a copyright strike, and won't impact your live broadcast, but it's still something to be concious of.
For example, if you check out any of my Beat Saber VoDs, entire sections of them are muted because of copywritten music! It doesn't affect my live broadcast though so.
I use a lot of copywritten video game music in my background music and I've never had a problem with that. I suppose it's because video game ost copywrightes aren't enforced as much, tbh. There are a lot of sources for copywright free music though, and a lot of games these days are implementing Stream Modes, which cut out copywritten music