fix(core): implement ChatPromptTemplate.save() method (#32637)

Remove NotImplementedError override in ChatPromptTemplate.save() to allow the
parent BasePromptTemplate implementation to handle serialization. ChatPromptTemplate
already has the required _prompt_type property ('chat') for proper serialization.

This enables users to save and load ChatPromptTemplate instances to/from YAML
and JSON files, matching the functionality of PromptTemplate and
FewShotPromptTemplate.

Changes:
- Remove NotImplementedError override from ChatPromptTemplate.save()
- Add comprehensive test for save/load roundtrip with both YAML and JSON formats

Fixes #32637

Author: Cwarre33

libs/core/langchain_core/prompts/chat.py

@@ -1273,14 +1273,6 @@ def _prompt_type(self) -> str:
         """Name of prompt type. Used for serialization."""
         return "chat"
 
-    def save(self, file_path: Path | str) -> None:
-        """Save prompt to file.
-
-        Args:
-            file_path: path to file.
-        """
-        raise NotImplementedError
-
     @override
     def pretty_repr(self, html: bool = False) -> str:
         """Human-readable representation.