At the same time, all other apps are at a level that won't cause painful audio to hit your ears.
If you trust VLC and you trust the video file you're watching, then turn the master audio back up during the loud "Universal Pictures" intro or whatever is an equivalent introductory sound at the beginning of the movie you're about to watch.
On my chromebook, there are two volume buttons and one mute button that are by far the most convenient way to adjust (master) audio for such a situation. So you turn down for random browsing and turn up for watching movies or whatever.
Btw-- those are almost certainly the controls someone would use to turn down or mute the sound of that horrible website audio listed above. In such a case the fact that pulse can give you an app volume for Chrome doesn't help anything-- for example, the user who adjusted Pulse app volume down to avoid pain will need to adjust it back up when watching a movie on Youtube for the same reason you mentioned. But they can't adjust the app volume with the keyboard controls. So to make use of that feature forces a more complicated UI that takes longer to use.
Then you tell your movie player to just make it louder, discarding that beautiful dynamic range. If you're paying close enough attention to the movie to care about the loss of dynamic range, then you probably aren't doing something else that might make sound, so you won't mind turning the master volume up.
So how do you ensure that one tab wasn't much louder than the other?
In this case, it doesn't make much sense to treat the browser as a single application, but each site as one (does Chrome export each tab as a separate source to PA? IDK, I haven't checked). And, I can't think of a single thing that I actually want producing sound (and don't mind just muting) from my web browser that doesn't have its own volume control.