feat(inference): Add BagelNet provider for Python client integration

[data-mission]

Summary

Implements Python client integration for BagelNet provider, following the HuggingFace Inference Providers integration process (Step 5).

Changes

• Add BagelNetConversationalTask provider implementation
• Register provider in PROVIDER_T and PROVIDERS with alphabetical ordering
• Update InferenceClient docstring to document BagelNet provider
• Add BagelNet entry to HARDCODED_MODEL_INFERENCE_MAPPING
• Add unit tests for BagelNet provider

Implementation Details

• Provider: bagelnet
• Base URL: https://api.bagel.net
• Task: conversational (OpenAI-compatible chat completions)
• Pattern: Follows cerebras.py minimal implementation approach

Prerequisites Completed

• JavaScript client integration (PR submitted)
• Model mapping API access (pending HF response)
• Billing endpoint implemented
• API infrastructure live at https://api.bagel.net

Related Work

• JavaScript client integration: feat(inference): Add BagelNet inference provider support huggingface.js#1574

Testing

• Unit tests included for provider initialization and inheritance
• Follows HF testing patterns for conversational providers
• No method overrides needed - uses default OpenAI-compatible behaviour

[data-mission]

Hi @Wauplin @julien-c @Narsil! 👋

This PR adds BagelNet provider support for Python client integration (Step 5 of the inference providers process).

Would appreciate your review when you have a chance. Thanks!