I put it into safe mode, and deleted a couple of video apps. I was able to play a YouTube video while looking at another page. But when I went back to normal mode, it happened again. So, how do I figure out which apps are causing the problem? Is there a type of app I should uninstall first?
Safe mode isn't going to help you. if you open up another tab while another tab is playing music then the tab playing music will stop. Only way would be to use pop-up view then reopen your browser app
Good, that means nothing is wrong with your phone. I'm not sure what's the best and fastest way to figure out which app is causing the issue, but if it were me I'd force stop the third party app one by one