I mean once the user selects a video you need to continue showing them context, because at this point they may not remember what mode they're in to begin with.
Making your app behave differently because you navigated to the current state via different menus is very bad UX design. That's all I'm saying. Your suggestion would entail either UX complexity or such implicitly different behavior for YouTube.
Yes Android has a "Home" button. But what I meant by no real UX equivalent is that when you open youtube on the web you'll open a new tab and go to youtube.com.
When you do so an Android you've likely just dismissed the app in the past, and opening it again will bring you back to the last video you were viewing. You don't go through the homepage by default.
Thus it's more of just another menu item on Android, not something that's equivalent to / on a website.