chore: bump chromium to 116.0.5845.0 (main) (#38827)

* chore: bump chromium in DEPS to 116.0.5835.0

* chore: update patches

* chore: bump chromium in DEPS to 116.0.5837.0

* chore: bump chromium in DEPS to 116.0.5839.0

* chore: bump chromium in DEPS to 116.0.5841.0

* chore: bump chromium in DEPS to 116.0.5843.0

* Update patches

CLs that affected printing.patch:
- 4616791: Refactor PrintViewManagerBase::PrintNow()
  4616791
- 4602776: Make PrintNodeUnderContextMenu operation go through PrintViewManager
  4602776

* 4506614: geolocation: Add LocationProvider::FillDiagnostics
4506614

* chore: bump chromium in DEPS to 116.0.5845.0

* chore: update patches

* fixup! 4506614: geolocation: Add LocationProvider::FillDiagnostics 4506614

* 4609704: Remove gnome-keyring
4609704

---------

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: clavin <clavin@electronjs.org>

patches/chromium/expose_setuseragent_on_networkcontext.patch

@@ -51,7 +51,7 @@ index 0ffa0ec042bd59de5d28fad53dee2b6321d64b18..a6570cb144952a1bb7eca124bb4cbb33
    // This may only be called on NetworkContexts created with the constructor
    // that calls MakeURLRequestContext().
 diff --git a/services/network/network_context.h b/services/network/network_context.h
-index f3a89933fef78c62e4c67fcfd521c8413c32e38f..8497ad66f2344b0379b8033d26ca2b87fa134294 100644
+index f10414f382b48ecc162b22d9638d948e3e719733..47d13dbe9efd501efabe096607e53cb80744cd42 100644
 --- a/services/network/network_context.h
 +++ b/services/network/network_context.h
 @@ -316,6 +316,7 @@ class COMPONENT_EXPORT(NETWORK_SERVICE) NetworkContext