[iOS] Update public Browser target.

This CL adds BrowserObserver to the public Browser target and updates
some BUILD.gn files to reference the public target.

Bug: none
Change-Id: I78a009fb6569121cd745f7f5771c43c1c538f24d
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/1972586Reviewed-by: Rohit Rao <rohitrao@chromium.org>
Commit-Queue: Kurt Horimoto <kkhorimoto@chromium.org>
Auto-Submit: Kurt Horimoto <kkhorimoto@chromium.org>
Cr-Commit-Position: refs/heads/master@{#726014}

ios/chrome/browser/main/BUILD.gn

@@ -5,6 +5,7 @@
 source_set("public") {
   sources = [
     "browser.h",
+    "browser_observer.h",
     "browser_user_data.h",
   ]
   deps = [
@@ -19,7 +20,6 @@ source_set("main") {
     "browser_agent_util.mm",
     "browser_impl.h",
     "browser_impl.mm",
-    "browser_observer.h",
     "browser_web_state_list_delegate.h",
     "browser_web_state_list_delegate.mm",
   ]
@@ -31,6 +31,7 @@ source_set("main") {
   deps = [
     "//base",
     "//ios/chrome/browser/browser_state",
+    "//ios/chrome/browser/infobars:badge",
     "//ios/chrome/browser/sessions:serialisation",
     "//ios/chrome/browser/sessions:session_service",
     "//ios/chrome/browser/tabs",

ios/chrome/browser/overlays/BUILD.gn

@@ -44,7 +44,7 @@ source_set("overlays") {
 
   deps = [
     "//base",
-    "//ios/chrome/browser/main",
+    "//ios/chrome/browser/main:public",
     "//ios/chrome/browser/web_state_list",
     "//ios/web/public",
   ]

ios/chrome/browser/ui/coordinators/BUILD.gn

@@ -12,6 +12,6 @@ source_set("chrome_coordinators") {
 
   deps = [
     "//base",
-    "//ios/chrome/browser/main",
+    "//ios/chrome/browser/main:public",
   ]
 }