feat(azure): add Responses API support for Azure OpenAI provider

[kunalk16]

Closes: #5202

Summary
Adds support for OpenAI's Responses API to the Azure OpenAI provider. Users can now opt in by setting api="responses" when creating an LLM instance. The existing Chat Completions API path remains the default and is completely untouched.

The Responses API is OpenAI's recommended API for new development, replacing Chat Completions as the primary interface. Azure OpenAI has adopted it with full feature parity.

# Example 1 basic
llm = LLM(model="azure/gpt-5.4-mini", api="responses")

# Example 2 with instructions
llm = LLM(model="azure/gpt-5.4-mini", api="responses", instructions="Be concise.")

Click to view Testing Details

Smoke Testing using the below test script:

from crewai import LLM

API_KEY = "api-key"
ENDPOINT = "https://some-internal-name.openai.azure.com"
MODEL = "azure/gpt-5.4-mini"

llm = LLM(
    model=MODEL,
    api="responses",
    api_key=API_KEY,
    endpoint=ENDPOINT,
)

print("=== Basic call ===")
result = llm.call(messages=[{"role": "user", "content": "Say hello in one sentence."}])
print(result)

print("\n=== Reasoning (medium) ===")
llm_reason = LLM(
    model=MODEL,
    api="responses",
    api_key=API_KEY,
    endpoint=ENDPOINT,
    reasoning_effort="medium",
)
result = llm_reason.call(messages=[{"role": "user", "content": "What is 47 * 83?"}])
print(result)

print("\n=== Multi-turn conversation ===")
llm_chat = LLM(
    model=MODEL,
    api="responses",
    api_key=API_KEY,
    endpoint=ENDPOINT,
    auto_chain=True,
    store=True,
)
r1 = llm_chat.call(messages=[{"role": "user", "content": "My favorite color is blue. Remember this."}])
print(f"Turn 1: {r1}")
r2 = llm_chat.call(messages=[{"role": "user", "content": "What is my favorite color?"}])
print(f"Turn 2: {r2}")
llm_chat.reset_chain()

print("\nDone!")

Test Output:

[kunalk16]

@joaomdmoura / @iris-clawd Requesting to kindly review this PR. It has been tested and all the repo rules have been followed.

[kunalk16]

@joaomdmoura / @greysonlalonde / @iris-clawd / @lucasgomide / @lorenzejay / @alex-clawd
Hello Reviewers,
Sorry for tagging like this but I'm not sure how to communicate this. I would really appreciate if you could have a look at this PR and review. It is a simple and useful change.

[kunalk16]

@joaomdmoura / @greysonlalonde / @iris-clawd / @lucasgomide / @lorenzejay / @alex-clawd
Hello Reviewers,
Sorry for tagging like this but I'm not sure how to communicate.
I would really appreciate if you could have a look at this PR and review. It is a simple and useful change. Please ack this.