chore: bump chromium to 116.0.5829.0 (main) (#38726)

* chore: bump chromium in DEPS to 116.0.5823.0

* chore: update patches

* chore: bump chromium in DEPS to 116.0.5825.0

* chore: update patches

* chore: bump chromium in DEPS to 116.0.5827.0

* chore: update patches

* 4568811: Integrate Search Prefetch with Extensions.

4568811

* 4567511: [DevTools] Add recordCountHistogram API.

4567511

* 4507692: Delete base/guid.h

4507692

* 4589551: Convert some of /base to use ARC

4589551
Also:
4601769: Convert immersive mode controllers to use ARC
4601769

* [viz] Convert MaybeSizeInBytes() to take in SharedImageFormat

4594677

* 4564108: [BRP] Enable check_raw_ptr_fields for Mac

4564108

* chore: bump chromium in DEPS to 116.0.5828.0

* chore: bump chromium in DEPS to 116.0.5829.0

* chore: update patches

---------

Co-authored-by: electron-roller[bot] <84116207+electron-roller[bot]@users.noreply.github.com>
Co-authored-by: PatchUp <73610968+patchup[bot]@users.noreply.github.com>
Co-authored-by: John Kleinschmidt <jkleinsc@electronjs.org>

patches/chromium/process_singleton.patch

@@ -51,7 +51,7 @@ index b05c0157ecca222452fb38e3b28c9d7cc6bcfbfd..02d9eabfef9521722340739bf86df3df
    base::win::MessageWindow window_;  // The message-only window.
    bool is_virtualized_;  // Stuck inside Microsoft Softricity VM environment.
 diff --git a/chrome/browser/process_singleton_posix.cc b/chrome/browser/process_singleton_posix.cc
-index e1a955c90d6c9f2d5caf18c6bb32e5a388d566be..5330402b1df783b8258b09d8e8dfc2cdf3819437 100644
+index c7c8f4c7f89073990c8fd6269ab83e75abd9ad7d..7cd73bf6d1884bd9b38bcb33de009efb1da2add9 100644
 --- a/chrome/browser/process_singleton_posix.cc
 +++ b/chrome/browser/process_singleton_posix.cc
 @@ -54,6 +54,7 @@