Cleanup uses of OpenAIMixin, simplify inference adapters

[mattf]

🤔 What is the technical debt you think should be addressed?

Provider	chat completions	completions	embedding	models: register	models: listing	models: availability	models: refresh	models: allowed	provider-data: key	config: key	config: url	health
anthropic	mixin	mixin	mixin	mixin	mixin	mixin	default	mixin	mixin	ANTHROPIC_API_KEY	n/a	no
azure openai	mixin	mixin	mixin	mixin	mixin	mixin	default	mixin	mixin	AZURE_API_KEY	AZURE_API_BASE, /openai/v1 added in provider	no
cerebras	mixin	mixin	disabled	mixin	mixin	mixin	default	mixin	no	CEREBRAS_API_KEY	coded in config, /v1 added in provider	no
databricks	mixin	disabled	mixin	mixin	mixin (not async)	mixin	false	mixin	no	DATABRICKS_TOKEN	DATABRICKS_HOST, extended as needed in provider	no
fireworks	mixin	mixin	mixin	mixin	mixin	mixin	default	mixin	mixin	FIREWORKS_API_KEY	coded in config and provider	no
gemini	mixin	mixin	mixin	mixin	mixin	mixin	default	mixin	mixin	GEMINI_API_KEY	coded in provider	no
groq	mixin	mixin	mixin	mixin	mixin	mixin	default	mixin	mixin	GROQ_API_KEY	coded in config, /openai/v1 added in provider	no
llama api	mixin	disabled	disabled	mixin	mixin	mixin	default	mixin	mixin	LLAMA_API_KEY	coded in config	no
nvidia	mixin	mixin	custom (for input_type)	mixin	mixin	mixin	default	mixin	no	NVIDIA_API_KEY	NVIDIA_BASE_URL, /v1 added in provider	no
ollama	mixin	mixin	mixin	custom (for :latest)	mixin	mixin	config	mixin	no	n/a	OLLAMA_URL w/ default, /v1 added	yes
openai	mixin	mixin	mixin	mixin	mixin	mixin	default	mixin	mixin	OPENAI_API_KEY	OPENAI_BASE_URL	no
runpod	custom (for stream usage)	mixin	mixin	mixin	mixin	mixin	default	mixin	no	RUNPOD_API_TOKEN	RUNPOD_URL (no default, no mods)	no
sambanova	mixin	mixin	mixin	mixin	mixin	mixin	default	mixin	mixin	SAMBANOVA_API_KEY	coded in config	no
tgi	mixin	mixin	disabled	mixin	mixin	mixin	default	mixin	no	n/a	TGI_URL	no
together	mixin	mixin	custom (for api incompatibility)	mixin	mixin	mixin	true	mixin	mixin	TOGETHER_API_KEY	coded in config	no
vertexai	mixin	mixin	mixin	mixin	mixin	mixin	default	mixin	mixin	GOOGLE_APPLICATION_CREDENTIALS	provider constructed from VERTEX_AI_PROJECT & VERTEX_AI_LOCATION	no
vllm	custom (for tool_choice)	mixin	mixin	mixin	mixin	mixin	config	mixin	mixin	VLLM_API_TOKEN w/ fake default	VLLM_URL	yes
watsonx - #3674	litellm	litellm	litellm	litellm	custom	custom (always True)	default	no	litellm	WATSONX_API_KEY	WATSONX_BASE_URL w/ default, also WATSONX_PROJECT_ID	no

TODO: bedrock, hf::serverless, hf::endpoints

💡 What is the benefit of addressing this technical debt?

maintainability.

Other thoughts

No response