Retry mechanism of Classic Duo Chat for Anthropic Overloaded error is not working
## Description
It seems that our retry mechanism of Classic Duo Chat for Anthropic Overloaded error is not working, currently. The error is supposed to be caught at [here](https://gitlab.com/gitlab-org/modelops/applied-ml/code-suggestions/ai-assist/-/blob/main/ai_gateway/chat/agents/react.py#L230) and notify clients to retry the request, however, it's currently raising hard error hence users are seeing `A1004` error code in Classic Duo Chat. i.e. regression of https://gitlab.com/gitlab-org/gitlab/-/issues/493507. This caused a production incident https://gitlab.slack.com/archives/C0A3XC9K8Q4/p1765938640331139.
This could be due to our recent switch to LiteLLM that altered the error message that it doesn't contain `overloaded_error` anymore. [example](https://log.gprd.gitlab.net/app/r?l=DISCOVER_SINGLE_DOC_LOCATOR&v=8.17.3&lz=N4IglgdgJgpgHiAXCAHAYygTjQFjQBgFoAzfAQwHZCBGamKQs%2Faq%2FKAZgCZqV8Ajau0z4QAGhAAnAPYB3AJLR4SEAAcArnwDOGwgFsANlJWbCkYoQDmKiQ3x3BKMZNlyoygMIAFTCoBSAVk0AISCATwBNOAAvfwArFAARTQsANicJGGIYCQyJZQB6MhUVfKgwTTQpADdsgGJ8gH4AfQsAXgALAAE0FPxOKH8UADImsg7O9nx2PEw3AF8gA%3D%3D) that indicates the exception message is now `litellm.ServiceUnavailableError: litellm.MidStreamFallbackError: litellm.InternalServerError: AnthropicError - Overloaded Original exception: InternalServerError: litellm.InternalServerError: AnthropicError - Overloaded`.
## Proposal
Make sure that the retry works with LiteLLM.
## Further details
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issue