### Check for existing issues

- [x] I have searched the existing issues and checked that my issue is not a duplicate.

### What happened?

I have a setup with OWUI -> LiteLLM. The gpt-5.6 serie works when i use the `mode: responses` definition in the model list. Else with the `mode: chat` i get an error saying "i cant use function call and reasoning in /v1/chat/completion".

My issue is that the sync with the price table also overwrites my definition of the mode: responses back to mode: chat ... But i would like to force GPT-5.6 be served with mode: responses. As a user i find this behavior unexpected and error-prone. I click on "price-refresh" and my setup is destroyed ... . Should the sync of prices really overwrite all explicit model config settings? As a user i would expect that it just defines the default values if i don't set anything.

### Steps to Reproduce

1. Define a gpt-5.6 model in the model_list like: ```yaml - model_name: 'openai.gpt-5.6-luna' litellm_params: model: 'openai/gpt-5.6-luna' api_base: os.environ/OPENAI_API_BASE api_key: os.environ/OPENAI_API_KEY model_info: access_groups: ["openai-models"] mode: responses a…