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931ce8d0 - core[patch]: Update `AsyncCallbackManager` to honor `run_inline` attribute and prevent context loss (#26885)

core[patch]: Update `AsyncCallbackManager` to honor `run_inline` attribute and prevent context loss (#26885) ## Description This PR fixes the context loss issue in `AsyncCallbackManager`, specifically in `on_llm_start` and `on_chat_model_start` methods. It properly honors the `run_inline` attribute of callback handlers, preventing race conditions and ordering issues. Key changes: 1. Separate handlers into inline and non-inline groups. 2. Execute inline handlers sequentially for each prompt. 3. Execute non-inline handlers concurrently across all prompts. 4. Preserve context for stateful handlers. 5. Maintain performance benefits for non-inline handlers. **These changes are implemented in `AsyncCallbackManager` rather than `ahandle_event` because the issue occurs at the prompt and message_list levels, not within individual events.** ## Testing - Test case implemented in #26857 now passes, verifying execution order for inline handlers. ## Related Issues - Fixes issue discussed in #23909 ## Dependencies No new dependencies are required. --- @eyurtsev: This PR implements the discussed changes to respect `run_inline` in `AsyncCallbackManager`. Please review and advise on any needed changes. Twitter handle: @parambharat --------- Co-authored-by: Eugene Yurtsev <eyurtsev@gmail.com>