[Android] Extract manager opening logic to interface/impl

Chromium change:
https://chromium.googlesource.com/chromium/src/+/65edd13188a0eb01fa8e1140b7489a40ee517d52

[bookmarks] Extract manager opening logic to interface/impl

The implementation of this interface can't be modularized. Extracting
the BookmarkUtils methods to an interface/impl combo which can
be used by classes in the bookamrks module.

Bug: 395908100

android/java/apk_for_test.flags

@@ -202,7 +202,6 @@
 
 -keep class org.chromium.chrome.browser.bookmarks.BookmarkUtils {
     *** addOrEditBookmark(...);
-    *** showBookmarkManagerOnPhone(...);
     *** isSpecialFolder(...);
 }