Reland "WebLocks: Remove unused include from lock_manager.h."

This is a reland of 264654a0749006cc756035d9ec444d0afeebf36a

The CL was reverted speculatively in https://crrev.com/c/2095733 to get
the tree green. The compilation errors leading to tree closure did not
seem related to the files changed in this CL.

Original change's description:
> WebLocks: Remove unused include from lock_manager.h.
>
> //content/browser/locks/lock_manager.h included
> //content/public/browser/browser_context.h, despite not using
> BrowserContext at all.
>
> Because lock_manager.h is included in storage_partition_impl.h,
> browser_context.h was indirectly included in many files. This CL fixes
> the IWYU violations highlighted by compiler errors.
>
> Change-Id: I46462b337d93a7ae1d60648cfd617b2e69662637
> Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/2093553
> Commit-Queue: Matt Falkenhagen <falken@chromium.org>
> Auto-Submit: Victor Costan <pwnall@chromium.org>
> Reviewed-by: Matt Falkenhagen <falken@chromium.org>
> Cr-Commit-Position: refs/heads/master@{#749082}

Tbr: falken
Change-Id: Iaa1527e4190a577d58355275f6badbd1c26ab44f
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/2100010
Reviewed-by: Victor Costan <pwnall@chromium.org>
Commit-Queue: Victor Costan <pwnall@chromium.org>
Cr-Commit-Position: refs/heads/master@{#749512}