[Fizz] Apply View Transition Name and Class to SSR:ed View Transitions (#33332)

Stacked on #33330.

This walks the element tree to activate the various classes under
different scenarios. There are some edge case things that are a little
different since we can't express every scenario without virtual nodes.

The main thing that's still missing though is avoiding animating updates
if it can be contained to a layout or enter/exit/share if they're out of
the viewport. I.e. layout stuff.