Standardize Inference Providers to Use `OpenAIMixin`

[mattf]

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

When the inference providers were originally created, shared mixins like OpenAIMixin and LiteLLMOpenAIMixin did not exist. As a result, many providers implemented their own logic manually and inconsistently.

Now that these mixins are available and some providers have adopted them, we have a fragmented implementation across the codebase. This results in:

• Duplicated logic (e.g. for streaming, parameter handling, response formatting)
• Inconsistent behavior across providers
• Increased maintenance burden
• Higher likelihood of subtle bugs and divergent implementations

💡 What is the benefit of addressing this technical debt?

• Consistency: All inference providers follow the same behavior.
• Maintainability: Changes (e.g. API updates, bug fixes) can be made in one place.
• Reduced Duplication: Shared logic eliminates repeated code across providers.
• Scalability: Easier to onboard or implement new providers.
• Better Testing: Shared mixins can be tested centrally, increasing reliability.

Inference providers

provider	chat	completions	embeddings	status	notes
anthropic	yes	yes	yes	#3366
azure openai	yes	yes	yes	#3396
bedrock	yes	yes	no	#3748
cerebras	yes	yes	no	#3481
databricks	yes	no	no	#3500
fireworks	yes	yes	yes	#3480
gemini	yes	yes	yes	#3351
groq	yes	yes	yes	#3348
llama	yes	yes	yes	#2835
nvidia	yes	yes	yes	#2835
ollama	yes	yes	yes	#3395
openai	yes	yes	yes	#2835
runpod	yes	yes	yes	#3707
sambanova	yes	yes	yes	#3345
tgi	yes	yes	no	#3417
hf::serverless	yes	yes	no	TODO	BROKEN: #3415
hf::endpoints	yes	yes	no	TODO
together	yes	yes	yes	#3458
vertexai	yes	yes	no	#3377
vllm	yes	yes	no	#3404
watsonx	yes	yes	no	#3674	standardized on LiteLLMOpenAIMixin