feat: support configuring api_key and api_base via environment variables

[thereds11]

What does this PR do?

• Adds support for configuring litellm.api_key and litellm.api_base via environment variables LITELLM_API_KEY and LITELLM_API_BASE.

Why is this useful?

• Helps teams running LiteLLM in containerized or CI/CD environments
• Improves developer experience by enabling .env or runtime environment injection

What's included:

• Code change in __init__.py
• README.md section added under Usage

Happy to iterate on feedback!

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Name	Status	Preview	Comments	Updated (UTC)
litellm	✅ Ready (Inspect)	Visit Preview	💬 Add feedback	Apr 6, 2025 8:04pm

[ishaan-jaff]

please add a test here's the checklist: https://docs.litellm.ai/docs/extras/contributing_code#checklist-before-submitting-a-pr

[krrishdholakia]

Thanks for your work @freshman829. Can you explain the problem a bit more?

You can already set the env var for any provider specific credential

[thereds11]

Thanks for your work @freshman829. Can you explain the problem a bit more?

You can already set the env var for any provider specific credential

Sure! While litellm allows provider-specific env vars, this change standardizes base-level config (api_key, api_base) across deployments—especially useful in Docker/CI environments where we don’t want to hardcode values or rely on provider-specific keys unless necessary.

[thereds11]

please add a test here's the checklist: https://docs.litellm.ai/docs/extras/contributing_code#checklist-before-submitting-a-pr

Added unit testing for my update

[CLAassistant]

All committers have signed the CLA.