InsetsSourceProvider nullability cleanup

With the nullability analysis and annotations from [1], we can now
remove some unnecessary null checks from InsetsSourceProvider, to simplify
the control flow. Additionally, this adds some nullability annotations
on the InsetsSourceProvider fields and method arguments, and re-orders
the code to avoid some potential null pointer exceptions.

This also removes from unused code left from before shell transitions
were finalized, tracked in 202383002.

  [1]: I8a563aa8fa6003135c44efbb19393c5e53203d40

Flag: EXEMPT cleanup
Bug: 281029564
Test: presubmit
Change-Id: I806c24c416ac1e38a508cb8d28ccdeff0cb92f1f