This patch is a collection of various cleanups made in public headers:
- Cleaned up many unnecessary includes. It doesn't change total amount
  of header files we use in total by `sycl.hpp`, but makes our code
  cleaner
- Made it so there are no headers depending on `backend.hpp` and it is
  only included by `sycl.hpp`, so that we can make it an opt-in header
- Removed `types.hpp` in favor of direct use of `vector.hpp`
- Added missing includes and forward-declarations to places where we
  relied on implicit includes
- Moved certain helper function declarations/definitions to better
  places (common utils to utils headers, library-only declarations to
  library headers, etc.)

…udes-cleanup

…udes-cleanup