Refactor assistant service into modules

[mateicanavra]

Summary

• split slideshow assistant service into Anthropic client, patch orchestration, and repair helper modules with a barrel export
• updated API guidance and backend orchestration docs to reflect the modular assistant layout
• kept existing assistant handler behavior while reducing file size and clarifying structure

Testing

• bun run check-types
• bun run build
• bun test

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Codex Task