[WIP] Fix Ollama requirement in openai integration

[Copilot]

Thanks for assigning this issue to me. I'm starting to work on it and will keep this PR's description up to date as I form a plan and make progress.

Original prompt

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This section details on the original issue you should resolve

<issue_title>Ollama is required?</issue_title>
<issue_description>Hello, i am trying to use openai but it seems its requiring Ollama?

plexsync: Sending request to LLM service
Initialized music search with providers: brave_search
Using Ollama model 'qwen3:latest' for result extraction and tool selection
Searching for track info: Sicko Mode by Travis Scott from Astroworld
Unified search failed: Client.chat() got an unexpected keyword argument 'tools'
Found track info: {'title': 'Sicko Mode by Travis Scott from Astroworld', 'album': None, 'artist': ''}
Searching for track info: Pop Out by Polo G feat. Lil Tjay from Die a Legend
Unified search failed: Client.chat() got an unexpected keyword argument 'tools'
Found track info: {'title': 'Pop Out by Polo G feat. Lil Tjay from Die a Legend', 'album': None, 'artist': ''}
Searching for track info: Life Is Good by Future feat. Drake from High Off Life
Unified search failed: Client.chat() got an unexpected keyword argument 'tools'
</issue_description>

<agent_instructions>The current llm search implementation relies on Ollama. Can we extend it allow any OpenAI compatible API. Re use the llm configuration for the search</agent_instructions>

Comments on the Issue (you are @copilot in this section)

Fixes #110

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