core(patch):fix partial_variables not working with SystemMessagePromptTemplate (#20711)

- **Issue:**  close #17560
- @baskaryan, @eyurtsev

libs/core/langchain_core/prompts/chat.py

@@ -407,6 +407,8 @@ class _StringImageMessagePromptTemplate(BaseMessagePromptTemplate):
         cls: Type[_StringImageMessagePromptTemplateT],
         template: Union[str, List[Union[str, _TextTemplateParam, _ImageTemplateParam]]],
         template_format: str = "f-string",
+        *,
+        partial_variables: Optional[Dict[str, Any]] = None,
         **kwargs: Any,
     ) -> _StringImageMessagePromptTemplateT:
         """Create a class from a string template.
@@ -414,6 +416,7 @@ class _StringImageMessagePromptTemplate(BaseMessagePromptTemplate):
         Args:
             template: a template.
             template_format: format of the template.
+            partial_variables: A dictionary of variables that can be used too partially.
             **kwargs: keyword arguments to pass to the constructor.
 
         Returns:
@@ -421,10 +424,16 @@ class _StringImageMessagePromptTemplate(BaseMessagePromptTemplate):
         """
         if isinstance(template, str):
             prompt: Union[StringPromptTemplate, List] = PromptTemplate.from_template(
-                template, template_format=template_format
+                template,
+                template_format=template_format,
+                partial_variables=partial_variables,
             )
             return cls(prompt=prompt, **kwargs)
         elif isinstance(template, list):
+            if (partial_variables is not None) and len(partial_variables) > 0:
+                raise ValueError(
+                    "Partial variables are not supported for list of templates."
+                )
             prompt = []
             for tmpl in template:
                 if isinstance(tmpl, str) or isinstance(tmpl, dict) and "text" in tmpl: