[BUG] The default model name is shown while executing Public agents

[epamLDadayan]

The default model name is shown while executing Public agents

Steps to reproduce:

1. Publish an agent.
2. Open it.
3. Change the LLM model from the default to smth else. (example from gpt-4-mini to o4-mini)
4. Execute it.
5. Verify the results:

Actual Result: The default model is show in execution section.
Expected Result: The correctly selected model is shown in execution section.

Note: IN BE everything is correct.

[HawkQing1]

@epamLDadayan could you please test it again because I can't not reproduce it.

[HawkQing1]

@daniilmotsniy even the user has changed the model and the model is sent in predict event, BE still uses the default model of the agent.
42["chat_predict",{"user_input":"Generate test cases","llm_settings":{"model_name":"gpt-5","model_project_id":1},"project_id":1,"conversation_uuid":"4aa3abcf-4c9e-4c74-afbe-55616a6f93aa","question_id":"2930863b-8f2f-4371-a72c-ef01ac95c8b9","participant_id":16}]

42["chat_predict",{"type":"agent_llm_start","stream_id":"4aa3abcf-4c9e-4c74-afbe-55616a6f93aa","message_id":"bc0cfdb4-2cae-4eb1-b476-614dd51ef313","content":null,"response_metadata":{"tool_name":"Thinking step","tool_run_id":"30571e31-916c-456f-a5bc-71f59a7d6843","metadata":{"ls_provider":"openai","ls_model_name":"gpt-4o-2024-08-06","ls_model_type":"chat","ls_temperature":0.1,"ls_max_tokens":4096},"timestamp_start":"2025-09-05T03:04:33.700262+00:00"},"references":[],"sio_event":"chat_predict","created_at":"2025-09-05T03:04:33.700404Z"}]