While working through #699, I noticed that many API providers now support reasoning_effort as a parameter, with some variation.

Here's a list of currently supported providers and their API docs. I'll update this issue with preliminary research into the overall availability and use of a reasoning_effort type parameter.

• chat_anthropic() – Anthropic – https://docs.anthropic.com/en/api/messages
• chat_aws_bedrock() – AWS Bedrock – https://docs.aws.amazon.com/bedrock/latest/APIReference/API_runtime_Converse.html
• chat_azure_openai() – Azure OpenAI – https://learn.microsoft.com/en-us/azure/ai-services/openai/reference#chat-completions
• chat_cloudflare() – Cloudflare – https://developers.cloudflare.com/workers-ai/configuration/open-ai-compatibility/
• chat_cortex_analyst() – Snowflake Cortex Analyst – https://docs.snowflake.com/en/developer-guide/snowflake-rest-api/reference/cortex-analyst
• chat_databricks() – Databricks – https://docs.databricks.com/aws/en/machine-learning/foundation-model-apis/api-reference#chat-request
• chat_deepseek() – DeepSeek – https://platform.deepseek.com/api-docs/api/create-chat-completion
• chat_github() – GitHub Models – https://docs.github.com/en/rest/models/inference?apiVersion=2022-11-28
• chat_google_gemini() – Google Gemini – https://ai.google.dev/api/generate-content#method:-models.generatecontent
• chat_groq() – Groq – https://console.groq.com/docs/api-reference#chat-create
• chat_huggingface() – Hugging Face – https://huggingface.co/docs/inference-providers/en/index?python-clients=requests#http--curl
• chat_mistral() – Mistral – https://api.mistral.ai/v1/
• chat_ollama() – Ollama – https://github.com/ollama/ollama/blob/main/docs/api.md#generate-a-chat-completion
• chat_openai() – OpenAI – https://platform.openai.com/docs/api-reference/chat/create
• chat_openrouter() – OpenRouter – https://openrouter.ai/docs/api-reference/parameters
• chat_perplexity() – Perplexity – https://docs.perplexity.ai/api-reference/chat-completions-post
• chat_portkey() – PortkeyAI – https://portkey.ai/docs/product/ai-gateway/universal-api
• chat_snowflake() – Snowflake Cortex – https://docs.snowflake.com/en/user-guide/snowflake-cortex/cortex-llm-rest-api#api-reference
• chat_vllm() – vLLM – https://docs.vllm.ai/en/latest/serving/openai_compatible_server.html

Sidenote: should we store this list in the ellmer source somewhere? Or maybe in the first line of each R/provider-*.R file?