Add LLM rotation.

[horw]

Since few LLM clients were supported, it would be good to implement, for example, random rotation.
Also, if one LLM reply with an error, it should retry with another LLM

[github-actions]

🤖 I've analyzed this issue title and have a suggestion for improvement:

Current title: Add LLM rotation.
Suggested title: "Implement LLM rotation with fallback on errors"

[github-actions]

🤖 I've analyzed¹ this issue title and have a suggestion for improvement:

Current title: Add LLM rotation.
Suggested title: "Implement LLM failover and rotation for error handling"

Footnotes

1. Suggested by issue-title-ai ↩