[TG Sync] Introduce public/ subdirectory in components/saved_tab_groups

The //components/saved_tab_groups directory has grown large and
contains too many files. This CL separates out the publicly needed
files and moves them into //components/saved_tab_groups/public
subdirectory. The BUILD targets are still left unchanged as this is
a very large change in terms of number of
files. In the next CL, a separate target will be added for
//components/saved_tab_groups/public, which will be referenced
everywhere else outside of components.

In addition, also
1. Created a delegated/ subdirectory for tab group
sync delegate related files.
2. Added a DEPS file for chrome/browser/ui/tabs/saved_tab_groups/DEPS.

Other than that, this CL is a pure mechanical move of files and
doesn't contain any other functional changes.

BYPASS_LARGE_CHANGE_WARNING

Bug: 369624428
Change-Id: I8b5dcb29e85c0ca4171d82a4d045990449dc4612
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5890368
Reviewed-by: Gauthier Ambard <[email protected]>
Reviewed-by: Tommy Nyquist <[email protected]>
Commit-Queue: Shakti Sahu <[email protected]>
Reviewed-by: Rushan Suleymanov <[email protected]>
Cr-Commit-Position: refs/heads/main@{#1363122}
diff --git a/chrome/browser/prefs/browser_prefs.cc b/chrome/browser/prefs/browser_prefs.cc
index 8cbedb5..ef93688 100644
--- a/chrome/browser/prefs/browser_prefs.cc
+++ b/chrome/browser/prefs/browser_prefs.cc
@@ -168,7 +168,7 @@
 #include "components/proxy_config/pref_proxy_config_tracker_impl.h"
 #include "components/safe_browsing/content/common/file_type_policies_prefs.h"
 #include "components/safe_browsing/core/common/safe_browsing_prefs.h"
-#include "components/saved_tab_groups/pref_names.h"
+#include "components/saved_tab_groups/public/pref_names.h"
 #include "components/search_engines/search_engine_choice/search_engine_choice_service.h"
 #include "components/search_engines/template_url_prepopulate_data.h"
 #include "components/security_interstitials/content/insecure_form_blocking_page.h"