Closes #1904

This makes clang-format useful on those.

Also add a bunch of forgotten transitive includes, which otherwise
prevented compilation.

They're finally unnecessary, and will stop cluttering the application's
handle table.

This should speed up compile times a bit, as well as enable more liberal
use of forward declarations. (Due to SharedPtr not trying to emit the
destructor anymore.)

This is to support the removal of GetHandle soon