Add AI Badgr as OpenAI-compatible provider documentation

[miguelmanlyx]

Why are these changes needed?

Adds AI Badgr as an optional OpenAI-compatible provider following the existing documentation pattern used for Gemini and Llama API. Enables users to access budget-tier models through AutoGen's standard OpenAIChatCompletionClient.

Changes:

• Added AI Badgr section to models.ipynb tutorial with Budget/Utility labeling
• Documents tier-based model names (basic, normal, premium) as primary interface
• Includes power-user model mappings (phi-3-mini, mistral-7b, llama3-8b-instruct)
• Uses AIBADGR_API_KEY environment variable pattern

Example usage:

from autogen_core.models import UserMessage, ModelInfo
from autogen_ext.models.openai import OpenAIChatCompletionClient

model_client = OpenAIChatCompletionClient(
    model="premium",
    base_url="https://aibadgr.com/api/v1",
    model_info=ModelInfo(
        vision=False,
        function_calling=True,
        json_output=True,
        family="unknown",
        structured_output=False,
    ),
)

Related issue number

N/A

Checks

• I've included any doc changes needed for https://microsoft.github.io/autogen/. See https://github.com/microsoft/autogen/blob/main/CONTRIBUTING.md to build and test documentation locally.
• I've added tests (if relevant) corresponding to the changes introduced in this PR.
• I've made sure all auto checks have passed.

[miguelmanlyx]

@microsoft-github-policy-service agree [company="aibadgr"]

[miguelmanlyx]

@microsoft-github-policy-service agree company="aibadgr"