[REFACTOR]: Expand `handleDefaultStreamResponseV2` to Parse Reasoning Output

[angelplusultra]

LM Studio, Ollama, DeepSeek, and Lemonade each currently implement their own bespoke handleStream logic. Most of these implementations are nearly identical and could likely be consolidated into a reusable abstraction. We could extend the generic stream handler, handleDefaultStreamResponseV2, to support parsing reasoning output from these providers and then reuse it across their respective handleStream implementations.