inspector: Add style classes to the object list

We have a lot of space here now, so show some
useful information.
inspector: Plug a memory leak
Broadway: Remove display assumptions

In various places, the broadway backend was just using
the default display and assumed that it is the broadway
display. That may not be the case in a multi-backend world,
so instead iterate over all displays and use the first
broadway display - still not perfect, but enough to survive
for now.