Regresssion from bd8a7edbd2.

When the toolbar buttons are overridden with URL parameters, our computed set of
buttons will be wrong. Thus, compute it every time and check for the
differences.

🔥🔥🔥

Contributing all buttons in one place goes against the designs that we
set out at the beginning of the project's rewrite and that multiple of
us have been following since then.

- Move the toolbar to the filmstrip feature
- Use all the buttons from the toolbox feature