[Breaking] Don't drop trees during DART prediction by default (#5115)

* Simplify DropTrees calling logic

* Add `training` parameter for prediction method.

* [Breaking]: Add `training` to C API.

* Change for R and Python custom objective.

* Correct comment.

Co-authored-by: Philip Hyunsu Cho <chohyu01@cs.washington.edu>
Co-authored-by: Jiaming Yuan <jm.yuan@outlook.com>

tests/cpp/test_logging.cc

@@ -54,7 +54,7 @@ TEST(Logging, Basic) {
   ASSERT_NE(output.find("Test Log Console"), std::string::npos);
 
   args["silent"] = "False";
-  args["verbosity"] = "1";  // restore
+  args["verbosity"] = "2";  // restore
   ConsoleLogger::Configure({args.cbegin(), args.cend()});
 }