Audit: Review reasoning extraction fallback in chat message handling

[coderabbitai]

Context

This issue tracks a potential improvement in how reasoning content is extracted from chat messages.

Background

In PR #482, a suggestion was made to improve the reasoning extraction by adding a fallback mechanism or using the centralized helper function:

• Current implementation only extracts reasoning from finalMessage.parts without fallback
• A suggestion was made to either use the extractReasoningContent helper or reinstate the fallback

Investigation Needed

Before implementing the suggested change, we need to:

• Verify if the UI correctly handles undefined/null thinking parts
• Determine if the current implementation might lose data in edge cases
• Evaluate the impact of centralizing reasoning extraction logic

References

• Original PR discussion

CC @AndlerRL