Support openai-chat-completions vs openai-responses API

When you define your custom provider as provider_type=openai, Dirge assumes you want to query /v1/chat/completions - but in my case, I need to query /v1/responses (the new GPT-5+ endpoint). I can see in the source code that you support /v1/responses, but there is no way to dictate its usage when setting up a custom provider.

Backstory: I do not want to install codex, so here is an oauthproxy: https://pkg.go.dev/github.com/lu-zhengda/liteoauthllm -- but it only provides the /v1/responses endpoint (because that's what OpenAI itself provides)

"providers": {
        "openai-gpt-5.6-luna": {
            "model": "gpt-5.6-luna",
            "provider_type": "openai",
            "base_url": "http://127.0.0.1:8639/v1",
            "api_key": "_",
            "allow_insecure": true
        },
        "openai-gpt-5.6-sol": {
            "model": "gpt-5.6-sol",
            "provider_type": "openai",
            "base_url": "http://127.0.0.1:8639/v1",
            "api_key": "_",
            "allow_insecure": true
        }
}