Reland "Include bloat: don't include browser_process_platform_part.h in browser_process.h"

This is a reland of c8281a39146cc307096926d48e458a50927ee347
with more fixes for files that depended on headers they need being
included further up the include chain.

Original change's description:
> Include bloat: don't include browser_process_platform_part.h in browser_process.h
>
> Avoiding this include reduces the number of preprocessor tokens in
> browser_process.h from 1,336,923 to 359,170.
>
> TBR=antrim
>
> Bug: 1014009
> Change-Id: Icc613c2889a6ca5fd5dd4b55a6bdd6b2772bcd4f
> Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/1856965
> Commit-Queue: Hans Wennborg <[email protected]>
> Reviewed-by: Nico Weber <[email protected]>
> Cr-Commit-Position: refs/heads/master@{#705554}

TBR=thakis

Bug: 1014009
Change-Id: I54892ddf84bcd6686c398c9dabb3f7dcf671af24
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/1860335
Reviewed-by: Hans Wennborg <[email protected]>
Commit-Queue: Hans Wennborg <[email protected]>
Cr-Commit-Position: refs/heads/master@{#705891}
114 files changed