Just tested and QuickTime Player stayed open, not sure I've ever seen this happen.
Did you open and play back a video first? If you just open QuickTime Player and don't interact with it, it does stay open if you switch apps. If you open a video, then close it, the app closes if you switch to a different app. I just tried it again and that's how it behaved. (I'm running Catalina still, so they may have fixed it in Big Sur.)
Yup. Is this a recent change? I still need to use some 32 bit programs for work so I'm on macos 10.14.6 quicktime player 10.5
No idea. I've seen it behave this way for at least the past year. I just tried it on a different Mac and it behaves similarly, except this other Mac causes QT to open up the File Open dialog immediately on launch. (Version 10.5 of QuickTime player for me too. macOS 10.15.7 though.)
If you open up QuickTime Player and then play back a video, then close the video, as soon as you background the app, it auto-quits itself. I wonder if they made it behave this way at some point to get around a memory leak. It's such an unexpected thing and it infuriates me each time I encounter it.