[Docs] - Update LiteLLM Integration Docs

[ishaan-jaff]

Hi i'm the LiteLLM (https://github.com/BerriAI/litellm) maintainer. Made some improvements to the doc section on using litellm with logfire

[ishaan-jaff]

@Kludex @alexmojaki can I get a review on this PR ?

[codecov[bot]]

Codecov Report

All modified and coverable lines are covered by tests :white_check_mark:

Project coverage is 100.00%. Comparing base (c763236) to head (f4e7881). Report is 73 commits behind head on main.

Additional details and impacted files

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##              main      #333   +/-   ##
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  Coverage   100.00%   100.00%           
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  Files          119       119           
  Lines         8882      8885    +3     
  Branches      1157      1159    +2     
=========================================
+ Hits          8882      8885    +3     

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[Kludex]

Let me know when you have applied the comments @ishaan-jaff 🙏

[samuelcolvin]

I thought LiteLLM was a library to give introp between different LLMs, why does it need a proxy?

[Kludex]

@ishaan-jaff are you still interested here? If so, please apply comments, and reply the question above.

[Kludex]

@ishaan-jaff Happy to continue this PR if you have time to reply the comments here. 🙏

For now, I'll be closing this PR.