[breaking] Save booster feature info in JSON, remove feature name generation. (#6605)

* Save feature info in booster in JSON model.
* [breaking] Remove automatic feature name generation in `DMatrix`.

This PR is to enable reliable feature validation in Python package.

tests/python/test_dmatrix.py

@@ -180,7 +180,7 @@ class TestDMatrix:
 
         # reset
         dm.feature_names = None
-        assert dm.feature_names == ['f0', 'f1', 'f2', 'f3', 'f4']
+        assert dm.feature_names is None
         assert dm.feature_types is None
 
     def test_feature_names(self):