core: mustache ChatPromptTemplate input schema types nested variables as str, so as_tool rejects valid input

Finding: In an external report (not reproduced by KFA), a mustache-format ChatPromptTemplate with nested variables such as {{user.name}} and {{user.company}} renders correctly from nested dict input, but its generated input schema types the top-level variable as a string. As a result, as_tool() rejects the same nested input with a pydantic ValidationError, on langchain_core 1.4.8 and reportedly on master at a97910508 (Python 3.13.9, macOS arm64) [https://github.com/langchain-ai/langchain/issues/41169]. Reported symptom: get_input_jsonschema() on the chain returns a schema in which user is a plain string, and invoking the resulting tool with a nested dict fails with the error 'Input should be a valid string' (input_type=dict) [https://github.com/langchain-ai/langchain/issues/41169]. The reporter adds that a tool-calling model reading this schema would be told to send a string, so it would never send the nested object the template needs, and that schema consumers such as LangServe playgrounds would show the wrong shape [https://github.com/langchain-ai/langchain/issues/41169]. Reporter's hypothesis (not maintainer-confirmed): ChatPromptTemplate falls back to the generic BasePromptTemplate.get_input_schema(), which types top-level variables as str, while PromptTemplate already calls mustache_schema() to produce nested objects for mustache templates [https://github.com/langchain-ai/langchain/issues/41169]. The suggested direction is a mustache-aware get_input_schema on ChatPromptTemplate that merges the mustache_schema() of its mustache message templates. Caveat for any fix, per the reporter: with a nested schema, as_tool() hands nested values to the prompt as Pydantic model instances rather than dicts. The mustache renderer deliberately refuses to traverse non-dict objects, so fields render as empty strings without error. The reporter says PromptTemplate.as_tool() already does this today, returning 'Write a greeting for from .' [https://github.com/langchain-ai/langchain/issues/41169]. A schema-only change could therefore turn the visible ValidationError into silently blank output. Status: the issue is open. A non-maintainer commenter says they implemented a schema override plus a conversion of nested tool arguments back to plain dicts inside convert_runnable_to_tool, but states their PR was auto-closed; no PR link, commit, or release was supplied, so this is an unverified proposal [https://github.com/langchain-ai/langchain/issues/41169#issuecomment-6075723530]. No maintainer response is present in the supplied thread, and the supplied comment coverage may omit middle comments. Limitations: this is an external report with reporter-run output. There is no KFA reproduction, no confirmed fix, and no released fix. No workaround is source-backed.