[MT-TREE] Support prediction cache and model slicing. (#8968)

- Fix prediction range.
- Support prediction cache in mt-hist.
- Support model slicing.
- Make the booster a Python iterable by defining `__iter__`.
- Cleanup removed/deprecated parameters.
- A new field in the output model `iteration_indptr` for pointing to the ranges of trees for each iteration.

python-package/xgboost/core.py

@@ -17,6 +17,7 @@ from typing import (
     Any,
     Callable,
     Dict,
+    Generator,
     Iterable,
     List,
     Optional,
@@ -1756,6 +1757,10 @@ class Booster:
         sliced.handle = sliced_handle
         return sliced
 
+    def __iter__(self) -> Generator["Booster", None, None]:
+        for i in range(0, self.num_boosted_rounds()):
+            yield self[i]
+
     def save_config(self) -> str:
         """Output internal parameter configuration of Booster as a JSON
         string.