[Headless] Have public_deps chain reflect inclusion chain

components/printing/browser/BUILD.gn

Index: components/printing/browser/BUILD.gn
diff --git a/components/printing/browser/BUILD.gn b/components/printing/browser/BUILD.gn
index bddd3a67d52f7af953ffed21aad12bb33ddf0f4d..3cce73a764724e62086bc453d02f2483eee10c44 100644
--- a/components/printing/browser/BUILD.gn
+++ b/components/printing/browser/BUILD.gn
@@ -10,10 +10,13 @@ static_library("browser") {
     "print_manager_utils.h",
   ]
 
+  public_deps = [
+    "//content/public/browser",
+  ]
+
   deps = [
     "//base",
     "//components/printing/common",
-    "//content/public/browser",
     "//printing",
   ]
 }